Question 1

What is the present value of $150 received at the beginning of each year for 16 years? The first payment is received today. Use a discount rate of 9%, and round your answer to the nearest $10.

Accepted Answer

A

Question 2

Ingrid Birdman can earn a nominal annual rate of return of 12%, compounded semiannually. If Ingrid made 40 consecutive semiannual deposits of $500 each, with the first deposit being made today, how much will she accumulate at the end of Year 20? Round off to the nearest $1.

Accepted Answer

To solve this problem, we need to use the formula for the future value of an annuity:

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

where:
PMT = payment per period ($500)
r = nominal annual rate of return / number of compounding periods per year (12% / 2 = 6%)
n = total number of periods (40)

Plugging in the values, we get:

FV = $500 * [((1 + 0.06)^40 - 1) / 0.06] = $82,023.89

Rounding off to the nearest $1, we get an answer of $82,024. So, the best choice is C.

Question 3

What is the present value of an annuity of $12 received at the end of each year for seven years? Assume a discount rate of 11%. The first payment will be received one year from today (round to the nearest $1).

Accepted Answer

We can use the formula for the present value of an annuity: PV = A[(1 - (1 + r)^-n) / r], where PV is the present value, A is the annuity payment, r is the discount rate, and n is the number of periods. Plugging in the values, we get:
PV = 12[(1 - (1 + 0.11)^-7) / 0.11]
PV = $57 (rounded to the nearest $1)

Question 4

It is January 1st and Darwin Davis has just established an IRA (Individual Retirement Account). Darwin will put $1,000 into the account on December 31st of this year and at the end of each year for the following 39 years (40 years total). How much money will Darwin have in his account at the beginning of the 41st year? Assume that the account pays 12% interest compounded annually, and round to the nearest $1,000.

Accepted Answer

Using the formula for compound interest, we can find the future value of Darwin's IRA:
FV = P(1+r)^n
where P = $1,000, r = 0.12, and n = 40 (since he is contributing for 40 years).
FV = $1,000(1+0.12)^40
FV = $767,274.87
Rounding to the nearest $1,000, Darwin will have $767,000 in his IRA at the beginning of the 41st year. Therefore, the best choice is C.

Question 5

Your company has received a $50,000 loan from an industrial finance company. The annual payments are $6,202.70. If the company is paying 9% interest per year, how many loan payments must the company make?

Accepted Answer

The number of loan payments can be found using the formula for the present value of an annuity: $PV = PMT \times \left(\frac{1 - (1 + r)^{-n}}{r}\right)$, where PV is the present value (loan amount), PMT is the annual payment, r is the annual interest rate, and n is the number of payments. Rearranging the formula to solve for n gives: $n = \frac{\log(1 - \frac{PV \times r}{PMT})}{\log(1 + r)}$. Substituting the given values ($PV = 50,000$, $PMT = 6,202.70$, $r = 0.09$) into the formula and solving for n yields approximately 15 payments.

Question 6

Ordinary annuities assume that cash flows occur

Accepted Answer

Ordinary annuities assume that cash flows occur at the end of a period.

Question 7

What is the present value of an annuity of $27 received at the beginning of each year for the next six years? The first payment will be received today, and the discount rate is 10% (round to nearest $10).

Accepted Answer

The present value of an annuity due (first payment received today) can be calculated using the formula: $PV = Pmt \times \left(\frac{1 - (1 + r)^{-n}}{r}\right) \times (1+r)$, where Pmt is the payment amount, r is the discount rate, and n is the number of periods. Plugging in the values: $PV = 27 \times \left(\frac{1 - (1 + 0.10)^{-6}}{0.10}\right) \times (1+0.10)$, we get a present value of approximately $130 when rounded to the nearest $10.

Question 8

Charlie Stone wants to retire in 30 years, and he wants to have an annuity of $1,000 a year for 20 years after retirement. Charlie wants to receive the first annuity payment at the end of the 30th year. Using an interest rate of 10%, how much must Charlie invest today in order to have his retirement annuity (round to the nearest $10)?

Accepted Answer

To calculate the present value of an annuity, we need to use the formula:

PV = A * (1 - (1 / (1 + r)^n)) / r

Where PV is the present value, A is the annuity payment, r is the interest rate, and n is the number of payments.

In this case, Charlie wants to receive an annuity of $1,000 a year for 20 years after he retires in 30 years. So, the number of payments n is 20, and the first payment comes at the end of the 30th year, so we need to discount it back 30 years to calculate the present value.

r = 10% or 0.1
n = 20
A = $1,000

PV = $1,000 * (1 - (1 / (1 + 0.1)^20)) / 0.1 * (1 + 0.1)^-30
PV = $540.17

Therefore, Charlie needs to invest $540.17 today to have an annuity of $1,000 for 20 years after he retires in 30 years. Rounded to the nearest $10, the answer is $540.

Question 9

What is the present value of $300 received at the beginning of each year for five years? Assume that the first payment is not received until the beginning of the third year (thus the last payment is received at the beginning of the seventh year). Use a 10% discount rate, and round your answer to the nearest $1.00.

Accepted Answer

The present value of an annuity due can be calculated by first finding the present value of the annuity and then adjusting for the fact that payments are received at the beginning of each period. The present value of the annuity is calculated for years 3 to 7, and then discounted back to the present value at year 0.

Question 10

A commercial bank will loan you $17,500 for two years to buy a car. The loan must be repaid in 24 equal monthly payments. The annual interest rate on the loan is 6% of the unpaid balance. What is the amount of the monthly payments?

Accepted Answer

The monthly payment can be calculated using the formula for an installment loan payment, which is derived from the annuity formula. Given an annual interest rate of 6%, the monthly interest rate is 0.5% (6% divided by 12 months). Using the formula for the monthly payment $PMT = P \times \frac{r(1+r)^n}{(1+r)^n - 1}$, where $P$ is the principal amount ($17,500), $r$ is the monthly interest rate (0.5% or 0.005 as a decimal), and $n$ is the total number of payments (24), the calculation yields a monthly payment of approximately $775.61.

Question 11

You wish to borrow $2,000 to be repaid in 12 monthly installments of $170.30. The annual interest rate is

Accepted Answer

The answer of You wish to borrow $2,000 to be...

Question 12

As the number of monthly payments on a loan increases, the size of each payment ________ and the total interest paid over the life of the loan ________.

Accepted Answer

As the number of monthly payments on a loan increases, the size of each payment decreases because the total amount to be repaid is spread out over a longer period of time. However, the total interest paid over the life of the loan increases because the loan balance is outstanding for a longer period, so interest accrues for a longer period of time.

Question 13

Gina Dare, who wants to be a millionaire, plans to retire at the end of 40 years. Gina's plan is to invest her money by depositing into an IRA at the end of every year. What is the amount that she needs to deposit annually in order to accumulate $1,000,000? Assume that the account will earn an annual rate of 11.5%. Round off to the nearest $1.

Accepted Answer

This problem requires the use of the future value formula for an annuity. The formula is: FV = PMT x [(1 + r)^n - 1] / r, where FV is the future value, PMT is the annual payment, r is the interest rate, and n is the number of years. Using this formula with the given values, we get:

$1,000,000 = PMT x [(1 + 0.115)^40 - 1] / 0.115
$1,000,000 = PMT x 219.8933
PMT = $1,000,000 / 219.8933
PMT = $4,546.06

Rounding this off to the nearest dollar gives us Choice A: $1,497.

Question 14

What is the present value of an annuity of $100 received at the end of each year for seven years? The first payment will be received one year from today (round to nearest $10). The discount rate is 13%. To solve this problem with a financial calculator, the correct choice is

Accepted Answer

To find the present value of an annuity, we need to use the PV function on a financial calculator. The inputs for this function require us to know the number of periods (N), the interest rate per period (i), the payment per period (PMT), and the future value (FV). Since we are given the payment per period and the interest rate, we can use Choice A to solve for the present value (PV).

Question 15

If you have $20,000 in an account earning 8% annually, what constant amount could you withdraw each year and have nothing remaining at the end of five years?

Accepted Answer

To find the constant withdrawal amount, use the formula for the annuity payment: P = [r*PV] / [1 - (1 + r)^-n], where P is the payment, r is the interest rate, PV is the present value, and n is the number of periods. Plugging in the values: P = [0.08*20000] / [1 - (1 + 0.08)^-5] = $5,008.76.

Question 16

Francis Peabody just won the $89,000,000 California State Lottery. The lottery offers the winner a choice of receiving the winnings in a lump sum or in 26 equal annual installments to be made at the beginning of each year. Assume that funds would be invested at 7.65%. Francis is trying to decide whether to take the lump sum or the annual installments. What is the amount of the lump sum that would be exactly equal to the present value of the annual installments? Round off to the nearest $1.

Accepted Answer

The present value of an annuity formula is used to calculate the lump sum equivalent of the annual installments. Using the given interest rate of 7.65% and 26 installments, the present value is approximately $41,083,128.

Question 17

If you invest $750 every six months at 8% compounded semi-annually, how much would you accumulate at the end of 10 years?

Accepted Answer

The future value of an annuity formula is used here: FV = P * [(1 + r)^nt - 1] / r, where P is the payment amount ($750), r is the interest rate per period (0.08/2 = 0.04), n is the number of compounding periods per year (2), and t is the number of years (10). Plugging in these values gives the future value of the annuity, which is approximately $22,334.

Question 18

What is the present value of $27 received at the end of each year for five years? Assume a discount rate of 9%. The first payment will be received one year from today (round to the nearest $1).

Accepted Answer

The present value of an annuity can be calculated using the formula: PV = Pmt × [(1 - (1 + r)^-n) / r], where Pmt is the payment amount, r is the discount rate, and n is the number of periods. Plugging in the values: PV = $27 × [(1 - (1 + 0.09)^-5) / 0.09] ≈ $105.

Question 19

What is the present value of $250 received at the beginning of each year for 21 years? Assume that the first payment is received today. Use a discount rate of 12%, and round your answer to the nearest $10.

Accepted Answer

This problem involves calculating the present value of an annuity, which can be done using the formula PV = C * [(1 - (1+r)^(-n))/r], where PV is the present value, C is the periodic payment, r is the discount rate (expressed as a decimal), and n is the total number of payments. Plugging in the given values, we get PV = 250 * [(1 - (1+0.12)^(-21))/0.12] = $2,117. Since we are asked to round to the nearest $10, the answer is C: $2,117.

Question 20

When comparing annuity due to ordinary annuities, annuity due annuities will have higher

Accepted Answer

Annuity due annuities have higher present values because payments are made at the beginning of each period, which means they benefit from one additional period of compounding compared to ordinary annuities. They also have higher future values because the first payment is compounding for one additional period compared to ordinary annuities. However, annuity due annuities do not have higher annuity payments compared to ordinary annuities.

Quiz 6: The Time Value of Money-Annuities and Other Topics

What is the present value of $150 received at the beginning of each year for 16 years? The first payment is received today. Use a discount rate of 9%, and round your answer to the nearest $10.

Ingrid Birdman can earn a nominal annual rate of return of 12%, compounded semiannually. If Ingrid made 40 consecutive semiannual deposits of $500 each, with the first deposit being made today, how much will she accumulate at the end of Year 20? Round off to the nearest $1.

What is the present value of an annuity of $12 received at the end of each year for seven years? Assume a discount rate of 11%. The first payment will be received one year from today (round to the nearest $1) .

Your company has received a $50,000 loan from an industrial finance company. The annual payments are $6,202.70. If the company is paying 9% interest per year, how many loan payments must the company make?

Ordinary annuities assume that cash flows occur

What is the present value of an annuity of $27 received at the beginning of each year for the next six years? The first payment will be received today, and the discount rate is 10% (round to nearest $10) .

A commercial bank will loan you $17,500 for two years to buy a car. The loan must be repaid in 24 equal monthly payments. The annual interest rate on the loan is 6% of the unpaid balance. What is the amount of the monthly payments?

You wish to borrow $2,000 to be repaid in 12 monthly installments of $170.30. The annual interest rate is

As the number of monthly payments on a loan increases, the size of each payment and the total interest paid over the life of the loan .

What is the present value of an annuity of $100 received at the end of each year for seven years? The first payment will be received one year from today (round to nearest $10) . The discount rate is 13%. To solve this problem with a financial calculator, the correct choice is

If you have $20,000 in an account earning 8% annually, what constant amount could you withdraw each year and have nothing remaining at the end of five years?

If you invest $750 every six months at 8% compounded semi-annually, how much would you accumulate at the end of 10 years?

What is the present value of $27 received at the end of each year for five years? Assume a discount rate of 9%. The first payment will be received one year from today (round to the nearest $1) .

What is the present value of $250 received at the beginning of each year for 21 years? Assume that the first payment is received today. Use a discount rate of 12%, and round your answer to the nearest $10.

When comparing annuity due to ordinary annuities, annuity due annuities will have higher