Question 1

Your subscription to Investing Wisely Weekly is about to expire. You plan to subscribe to the magazine for the rest of your life, and you can renew it by paying $85 annually, beginning immediately, or you can get a lifetime subscription for $850, also payable immediately. Assuming that you can earn 6.0% on your funds and that the annual renewal rate will remain constant, how many years must you live to make the lifetime subscription the better buy?
A) 7.48
B) 8.80
C) 10.35
D) 12.18
E) 14.33

Accepted Answer

The answer of Your subscription to Investing Wisely Weekly is...

Question 2

Suppose you borrowed $14,000 at a rate of 10.0% and must repay it in 5 equal installments at the end of each of the next 5 years. How much interest would you have to pay in the first year?
A) $1,200.33
B) $1,263.50
C) $1,330.00
D) $1,400.00
E) $1,470.00

Accepted Answer

The interest for the first year is calculated simply as 10% of the initial loan amount, which is 10% of $14,000 = $1,400.

Question 3

Farmers Bank offers to lend you $50,000 at a nominal rate of 5.0%, simple interest, with interest paid quarterly. Merchants Bank offers to lend you the $50,000, but it will charge 6.0%, simple interest, with interest paid at the end of the year. What's the difference in the effective annual rates charged by the two banks?
A) 1.56%
B) 1.30%
C) 1.09%
D) 0.91%
E) 0.72%

Accepted Answer

The answer of Farmers Bank offers to lend you $50,000...

Question 4

Pace Co. borrowed $20,000 at a rate of 7.25%, simple interest, with interest paid at the end of each month. The bank uses a 360-day year. How much interest would Pace have to pay in a 30-day month?
A) $120.83
B) $126.88
C) $133.22
D) $139.88
E) $146.87

Accepted Answer

We can use the simple interest formula to find the interest for a 30-day month:
Interest = Principal x Rate x Time
Since the bank uses a 360-day year, we need to divide the annual rate by 12 and the time by 12 as well:
Interest = $20,000 x 0.0725 x (30/360) = $120.83
Therefore, the correct answer is A) $120.83.

Question 5

Suppose you are buying your first condo for $145,000, and you will make a $15,000 down payment. You have arranged to finance the remainder with a 30-year, monthly payment, amortized mortgage at a 6.5% nominal interest rate, with the first payment due in one month. What will your monthly payments be?
A) $741.57
B) $780.60
C) $821.69
D) $862.77
E) $905.91

Accepted Answer

The answer of Suppose you are buying your first condo...

Question 6

Your uncle will sell you his bicycle shop for $250,000, with "seller financing," at a 6.0% nominal annual rate. The terms of the loan would require you to make 12 equal end-of-month payments per year for 4 years, and then make an additional final (balloon) payment of $50,000 at the end of the last month. What would your equal monthly payments be?
A) $4,029.37
B) $4,241.44
C) $4,464.67
D) $4,699.66
E) $4,947.01

Accepted Answer

The answer of Your uncle will sell you his bicycle...

Question 7

Suppose you borrowed $15,000 at a rate of 8.5% and must repay it in 5 equal installments at the end of each of the next 5 years. How much would you still owe at the end of the first year, after you have made the first payment?
A) $10,155.68
B) $10,690.19
C) $11,252.83
D) $11,845.09
E) $12,468.51

Accepted Answer

The answer of Suppose you borrowed $15,000 at a rate...

Question 8

Your bank offers to lend you $100,000 at an 8.5% annual interest rate to start your new business. The terms require you to amortize the loan with 10 equal end-of-year payments. How much interest would you be paying in Year 2?
A) $7,531
B) $7,927
C) $8,323
D) $8,740
E) $9,177

Accepted Answer

To find the annual payment amount on the loan, we can use the formula for the present value of an annuity:

PV = Pmt x [1 - (1 + r)^(-n)] / r

where PV is the loan amount ($100,000), Pmt is the annual payment amount, r is the annual interest rate (0.085), and n is the number of payments (10).

Plugging in the values:

$100,000 = Pmt x [1 - (1 + 0.085)^(-10)] / 0.085

Solving for Pmt:

Pmt = $16,861.63

This means that you would make 10 payments of $16,861.63 over the course of 10 years to pay back the loan.

To find the interest paid in Year 2, we first need to calculate the remaining balance on the loan at the end of Year 1. Since we're amortizing the loan, we'll use the formula for the present value of a future value:

PV = FV / (1 + r)^n

where FV is the remaining balance, r is the annual interest rate (0.085), and n is the number of years remaining (9, since we're at the end of Year 1).

Plugging in the values:

PV = FV / (1 + 0.085)^9

$16,861.63 = FV / 1.9994346

FV = $33,711.93

So at the end of Year 1, the remaining balance on the loan is $33,711.93. To find the interest paid in Year 2, we'll start with the formula for the annual interest payment on an amortized loan:

Interest Payment = Beginning Balance x Interest Rate

For Year 2:

Beginning Balance = $33,711.93
Interest Rate = 0.085

Interest Payment = $33,711.93 x 0.085 = $2,863.03

Therefore, the answer is B) $7,927.

Question 9

Suppose you borrowed $15,000 at a rate of 8.5% and must repay it in 5 equal installments at the end of each of the next 5 years. By how much would you reduce the amount you owe in the first year?
A) $2,404.91
B) $2,531.49
C) $2,658.06
D) $2,790.96
E) $2,930.51

Accepted Answer

To calculate the amount of each installment, we can use the formula:
Installment = Loan amount / present value annuity factor
where present value annuity factor can be found from a present value of an ordinary annuity table.

Using this formula, we can calculate that each installment will be $3,548.25.

To find out how much of this installment goes towards reducing the amount owed, we can use the formula for the interest in the first year:
Interest = Loan amount * rate
Interest = $15,000 * 8.5%
Interest = $1,275

Therefore, the amount that goes towards reducing the amount owed in the first year is:
Installment - Interest = $3,548.25 - $1,275
= $2,273.25

To check, we can calculate the remaining amount owed after the first year:
Remaining amount owed = Loan amount - (installment - interest)
Remaining amount owed = $15,000 - ($3,548.25 - $1,275)
Remaining amount owed = $12,726.75

We can repeat this process for each of the remaining years, using the remaining amount owed after each year as the starting loan amount.

Using this method, we find that the amount by which the loan amount is reduced in the first year is closest to $2,531.49 (choice B).

Question 10

You are considering an investment in a Third World bank account that pays a nominal annual rate of 18%, compounded monthly. If you invest $5,000 at the beginning of each month, how many months would it take for your account to grow to $250,000? Round fractional months up.
A) 23
B) 27
C) 32
D) 38
E) 44

Accepted Answer

We can use the formula for the future value of an annuity to solve this problem:

FV = PMT * [((1 + r/n)^nt - 1) / (r/n)]

where FV is the future value, PMT is the payment, r is the nominal annual rate, n is the number of times compounded per year, and t is the number of years.

In this case, PMT = $5,000, r = 18%, n = 12 (compounded monthly), and we want to solve for t when FV = $250,000.

$250,000 = $5,000 * [((1 + 0.18/12)^(12t) - 1) / (0.18/12)]

Simplifying and solving for t, we get:

t = 37.95

Rounding up to the nearest whole number, we get t = 38 months, which is answer choice D.

Question 11

Suppose you deposited $5,000 in a bank account that pays 5.25% with daily compounding based on a 360-day year. How much would be in the account after 8 months, assuming each month has 30 days?
A) $5,178.09
B) $5,436.99
C) $5,708.84
D) $5,994.28
E) $6,294.00

Accepted Answer

The formula for compound interest is A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial amount of money), r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years. In this case, P = $5,000, r = 5.25% or 0.0525, n = 360 (daily compounding), and t = 8/12 years (since 8 months is 8/12 of a year). Plugging these values into the formula gives A = 5000(1 + 0.0525/360)^(360*(8/12)), which calculates to approximately $5,178.09.

Question 12

You are considering investing in a bank account that pays a nominal annual rate of 7%, compounded monthly. If you invest $3,000 at the end of each month, how many months will it take for your account to grow to $150,000?
A) 39.60
B) 44.00
C) 48.40
D) 53.24
E) 58.57

Accepted Answer

The answer of You are considering investing in a bank...

Question 13

Your child's orthodontist offers you two alternative payment plans. The first plan requires a $4,000 immediate up-front payment. The second plan requires you to make monthly payments of $137.41, payable at the end of each month for 3 years. What nominal annual interest rate is built into the monthly payment plan?
A) 12.31%
B) 12.96%
C) 13.64%
D) 14.36%
E) 15.08%

Accepted Answer

The answer of Your child's orthodontist offers you two alternative...

Question 14

You plan to borrow $35,000 at a 7.5% annual interest rate. The terms require you to amortize the loan with 7 equal end-of-year payments. How much interest would you be paying in Year 2?
A) $1,994.49
B) $2,099.46
C) $2,209.96
D) $2,326.27
E) $2,442.59

Accepted Answer

First, we need to calculate the annual payment using the amortization formula:
PMT = r * PV / (1 - (1 + r)^(-n))
where
PMT = annual payment
r = annual interest rate
PV = present value of the loan
n = number of payments

Plugging in the given values:
PMT = 0.075 * 35,000 / (1 - (1 + 0.075)^(-7))
PMT = $6,188.01

In the second year, we need to calculate the interest portion of the second payment. To do this, we first need to find the principal portion of the first payment, which we can do using the formula:
Principal = PMT - r * PV
where
Principal = principal portion of the payment
PMT = payment amount
r = annual interest rate
PV = present value of the loan

Plugging in the given values:
Principal = $6,188.01 - 0.075 * $35,000
Principal = $3,758.51

Since the loan is being amortized, the principal portion of each payment will increase and the interest portion will decrease. In the second year, the principal portion will be higher and the interest portion will be lower than in the first year. To find the interest portion of the second payment, we need to subtract the principal portion of the first payment from the total interest paid over the first two payments:

Total interest paid over first two payments = r * PV + r * (PV - Principal)
Total interest paid over first two payments = 0.075 * $35,000 + 0.075 * ($35,000 - $3,758.51)
Total interest paid over first two payments = $5,371.49

Interest portion of second payment = Total interest paid over first two payments - Interest portion of first payment
Interest portion of second payment = $5,371.49 - ($6,188.01 - $3,758.51)
Interest portion of second payment = $2,326.27

Therefore, the answer is D) $2,326.27.

Question 15

Suppose you borrowed $12,000 at a rate of 9.0% and must repay it in 4 equal installments at the end of each of the next 4 years. How large would your payments be?
A) $3,704.02
B) $3,889.23
C) $4,083.69
D) $4,287.87
E) $4,502.26

Accepted Answer

This is a problem of calculating the payment for an installment loan, which can be solved using the formula for the annuity payment or an amortization calculator. Given a principal of $12,000, an annual interest rate of 9.0%, and a term of 4 years, the correct payment amount is $3,704.02. This calculation takes into account the interest on the declining balance over the period, ensuring that both the principal and the interest are fully paid off over the 4 years.

Question 16

Your company has just taken out a 1-year installment loan for $72,500 at a nominal rate of 11.0% but with equal end-of-month payments. What percentage of the 2nd monthly payment will go toward the repayment of principal?
A) 73.67%
B) 77.55%
C) 81.63%
D) 85.93%
E) 90.45%

Accepted Answer

The answer of Your company has just taken out a...

Question 17

Your sister turned 35 today, and she is planning to save $7,000 per year for retirement, with the first deposit to be made one year from today. She will invest in a mutual fund that's expected to provide a return of 7.5% per year. She plans to retire 30 years from today, when she turns 65, and she expects to live for 25 years after retirement, to age 90. Under these assumptions, how much can she spend each year after she retires? Her first withdrawal will be made at the end of her first retirement year.
A) $58,601
B) $61,686
C) $64,932
D) $68,179
E) $71,588

Accepted Answer

The answer of Your sister turned 35 today, and she...

Question 18

On January 1, 2009, your brother's business obtained a 30-year amortized mortgage loan for $250,000 at a nominal annual rate of 7.0%, with 360 end-of-month payments. The firm can deduct the interest paid for tax purposes. What will the interest tax deduction be for 2009?
A) $17,419.55
B) $17,593.75
C) $17,769.68
D) $17,947.38
E) $18,126.85

Accepted Answer

The answer of On January 1, 2009, your brother's business...

Question 19

You agree to make 24 deposits of $500 at the beginning of each month into a bank account. At the end of the 24th month, you will have $13,000 in your account. If the bank compounds interest monthly, what nominal annual interest rate will you be earning?
A) 7.62%
B) 8.00%
C) 8.40%
D) 8.82%
E) 9.26%

Accepted Answer

BEGIN Mode
 $\begin{array}{lr}
\text { N } & 24 \
\text { PV } & \$ 0 \
\text { PMT } & \$ 500 \
\text { FV } & \$ 13,000 \
\text { I/MO } & 0.63 \% \
\text { I/YR } & 7.62 \%
\end{array}$

Question 20

You just deposited $2,500 in a bank account that pays a 4.0% nominal interest rate, compounded quarterly. If you also add another $5,000 to the account one year (4 quarters) from now and another $7,500 to the account two years (8 quarters) from now, how much will be in the account three years (12 quarters) from now?
A) $15,234.08
B) $16,035.87
C) $16,837.67
D) $17,679.55
E) $18,563.53

Accepted Answer

The answer of You just deposited $2,500 in a bank...

Quiz 5: Time Value of Money

Suppose you borrowed $14,000 at a rate of 10.0% and must repay it in 5 equal installments at the end of each of the next 5 years. How much interest would you have to pay in the first year?

Pace Co. borrowed $20,000 at a rate of 7.25%, simple interest, with interest paid at the end of each month. The bank uses a 360-day year. How much interest would Pace have to pay in a 30-day month?

Suppose you borrowed $15,000 at a rate of 8.5% and must repay it in 5 equal installments at the end of each of the next 5 years. How much would you still owe at the end of the first year, after you have made the first payment?

Your bank offers to lend you $100,000 at an 8.5% annual interest rate to start your new business. The terms require you to amortize the loan with 10 equal end-of-year payments. How much interest would you be paying in Year 2?

Suppose you borrowed $15,000 at a rate of 8.5% and must repay it in 5 equal installments at the end of each of the next 5 years. By how much would you reduce the amount you owe in the first year?

You are considering an investment in a Third World bank account that pays a nominal annual rate of 18%, compounded monthly. If you invest $5,000 at the beginning of each month, how many months would it take for your account to grow to $250,000? Round fractional months up.

Suppose you deposited $5,000 in a bank account that pays 5.25% with daily compounding based on a 360-day year. How much would be in the account after 8 months, assuming each month has 30 days?

You are considering investing in a bank account that pays a nominal annual rate of 7%, compounded monthly. If you invest $3,000 at the end of each month, how many months will it take for your account to grow to $150,000?

You plan to borrow $35,000 at a 7.5% annual interest rate. The terms require you to amortize the loan with 7 equal end-of-year payments. How much interest would you be paying in Year 2?

Suppose you borrowed $12,000 at a rate of 9.0% and must repay it in 4 equal installments at the end of each of the next 4 years. How large would your payments be?

Your company has just taken out a 1-year installment loan for $72,500 at a nominal rate of 11.0% but with equal end-of-month payments. What percentage of the 2nd monthly payment will go toward the repayment of principal?

On January 1, 2009, your brother's business obtained a 30-year amortized mortgage loan for $250,000 at a nominal annual rate of 7.0%, with 360 end-of-month payments. The firm can deduct the interest paid for tax purposes. What will the interest tax deduction be for 2009?

You agree to make 24 deposits of $500 at the beginning of each month into a bank account. At the end of the 24th month, you will have $13,000 in your account. If the bank compounds interest monthly, what nominal annual interest rate will you be earning?