Help is Here, a wrecker company, will soon need to purchase a new wrecker. The company anticipates needing $35,000 in 3 years. Their credit union offers an account that pays 3.4% per year, compounded monthly for 36 months. Find the monthly payment needed to accumulate the desired amount.

Question

13-01-2025
Business

High School

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Help is Here, a wrecker company, will soon need to purchase a new wrecker. The company anticipates needing $35,000 in 3 years. Their credit union offers an account that pays 3.4% per year, compounded monthly for 36 months. Find the monthly payment needed to accumulate the desired amount.

Answer :

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PeterGene PeterGene · Answer 1 · 2025-01-18T16:36:44-05:00

Final answer:

The question involves using the formula for the future value of an annuity due to calculate the monthly payment needed to accumulate $35,000 in 3 years at an annual interest rate of 3.4%, compounded monthly. It is important to rearrange the formula to solve for the monthly payment.

Explanation:

The question is asking to determine the monthly payment needed to accumulate $35,000 in 3 years in an account that pays 3.4% per year, compounded monthly. The formula to find the monthly payment for a future value with compound interest is derived from the future value of an annuity due formula:

Future Value (FV) = Payment (PMT) * [((1 + r)^n - 1) / r],

where FV is the future value we want to accumulate, PMT is the monthly payment we need to find out, r is the monthly interest rate, and n is the total number of payments.

To solve for PMT, we rearrange the formula to get:

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

We plug in the given values: FV = $35,000, the annual interest rate is 3.4% (which we divide by 12 to get the monthly rate), and n = 36 months (3 years' worth of months).

The exact calculation process would be to convert the annual interest rate to a monthly rate by dividing by 12, then applying the above formula to find the monthly payment that would result in the desired future value after 36 months.