Question 1

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 calculate the yearly payment, we can use the formula:
PMT = (P*r)/(1 - (1+r)^(-n))
where P is the loan amount, r is the annual interest rate, and n is the number of payments.
Plugging in the values, we get:
PMT = (100,000*0.085)/(1 - (1+0.085)^(-10)) = $16,216.28 per year
In Year 2, the outstanding balance would be:
B2 = (PMT/(1+r))^n-1 * (1+r)/r
where r is the annual interest rate and n is the number of years remaining.
Plugging in the values, we get:
B2 = ($16,216.28/(1+0.085))^8 * (1+0.085)/0.085 = $76,117.91
The interest paid in Year 2 would be:
I2 = r*B2 = 0.085*$76,117.91 = $6,471.39
However, we need to adjust this for the fact that the payment in Year 2 includes both principal and interest. Using the formula for the payment:
PMT = IPMT + PPMT
where IPMT is the interest portion and PPMT is the principal portion.
Plugging in the values, we get:
$16,216.28 = $6,471.39 + PPMT
PPMT = $9,744.89
Therefore, the interest paid in Year 2 would be:
I2 = $6,471.39 + $9,744.89 = $16,216.28 - $76,117.91 = $7,927.02, which is closest to option B ($7,927).

Question 2

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 3

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

Using the formula for the future value of an annuity, we can solve for the number of months required: 
$250,000 = $5,000 [(1+(0.18/12))^n - 1] / (0.18/12) 
n = 38.03 months 
Rounding up, it will take 38 months for the account to grow to $250,000.

Question 4

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...

Quiz 5: Time Value of Money

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?

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 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.