Asked by Jesus Armenta on May 05, 2024

Verified

(Ignore income taxes in this problem.) How much would you have to invest today in the bank at an interest rate of 8% to have an annuity of $4,800 per year for 7 years, with nothing left in the bank at the end of the 7 years? Select the amount below that is closest to your answer.

A) $33,600

B) $2,798

C) $24,989

D) $31,111

A) $33,600

B) $2,798

C) $24,989

D) $31,111

Annuity

A series of identical cash flows.

Interest Rate

The proportion of a loan that is charged as interest to the borrower, typically expressed as an annual percentage of the loan outstanding.

Invest Today

A strategy or encouragement to allocate resources, such as time or money, currently, with the expectation of future benefits.

- Analyze financial ventures by evaluating their present and anticipated values to make knowledgeable decisions.
- Comprehend the fundamentals of annuities and their assessment.

Verified Answer

DA

Darryl Anne Laurente

May 09, 2024

Final Answer :

C

Explanation :

This problem requires us to use the present value of an annuity formula, which is:

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

where PV is the present value, PMT is the annuity payment, r is the interest rate, and n is the number of periods.

In this case, PMT = $4,800, r = 8% or 0.08, and n = 7. The formula becomes:

PV = $4,800 * [(1 - (1 / (1 + 0.08)^7)) / 0.08] = $24,989

Therefore, you would have to invest $24,989 today to have an annuity of $4,800 per year for 7 years, with nothing left in the bank at the end of the 7 years. The closest choice to this answer is C) $24,989.

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

where PV is the present value, PMT is the annuity payment, r is the interest rate, and n is the number of periods.

In this case, PMT = $4,800, r = 8% or 0.08, and n = 7. The formula becomes:

PV = $4,800 * [(1 - (1 / (1 + 0.08)^7)) / 0.08] = $24,989

Therefore, you would have to invest $24,989 today to have an annuity of $4,800 per year for 7 years, with nothing left in the bank at the end of the 7 years. The closest choice to this answer is C) $24,989.

Explanation :

$4,800 × 5.206 = $24,988.80

## Learning Objectives

- Analyze financial ventures by evaluating their present and anticipated values to make knowledgeable decisions.
- Comprehend the fundamentals of annuities and their assessment.