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3 years ago

If the balance in the account 7 months after the final deposit is $8, 000, how large is each deposit?

Business

1 answer:

vampirchik [111]3 years ago

3 0

Answer:

the first part of the question is missing:

Suppose that you make a sequence of 31 equal monthly deposits into an account paying a nominal rate of 6.7% convertible quarterly.

we need to determine the present value of the $8,000 at the moment that you stop making the monthly payments.

the effective annual interest rate = (1 + 6.7%/4)⁴ - 1 = 6.87%

the effective monthly interest rate = (1 + 6.87%)¹/¹² - 1 = 0.55523%

the value at the moment that you finish making the deposits = $8,000 / (1 + 0.0055523)⁷ = $7,695.86

now we can calculate the monthly payments using the future value of an annuity formula:

future value = monthly payment x FV annuity factor

monthly payment = future value / FV annuity factor

future value = $7,695.86
FV annuity factor, 31 periods, 0.55523% = 33.72594

monthly payment = $7,695.86 / 33.72594 = $228.19

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