A small foundry agrees to pay $220,000 two years from now to a supplier for a given amount of coking coal. The foundry plans to deposit a fixed amount in a bank account every three months, starting three months from now, so that at the end of two years the account holds $220,000.

If the account pays 12.5% APR compounded monthly, how much must be deposited every three months?

A) $24,602

B) $27,063

C) $29,523

D) $31,983

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ajeigbeibraheem ajeigbeibraheem · Answer 1 · 2020-03-15T01:52:17+01:00

Answer:

A) $24,602

Explanation:

We can solve this question by finding the periodic deposits needed by using the formula:

[tex]FV=PMT*\frac{(1+i)^n-1}{i}[/tex]

where:

FV= future value = $220,000

PMT = periodic deposits required = ???

i = effective interest rate per period = 0.0331

n= number of deposits = 8

However, since the interest is compounded monthly, let's also calculate the effective interest rate

Effective interest rate = [tex](1+\frac{r}{m}) ^m-1[/tex]

where; r = 12.5% = 0.125

[tex](1+\frac{0.125}{12})^{12} -1[/tex]

= 0.1324

Interest rate per period = [tex]\frac{0.1324}{4}[/tex]

= 0.0331

Then;

[tex]220,000=PMT*\frac{(1+0.033)^8-1}{0.033}[/tex]

220,000 = PMT × 8.986

PMT = [tex]\frac{220,000}{8.986}[/tex]

PMT = $ 24,482.5

Since A) $24,602 is closer to $ 24,482.5

Therefore, $ $24,602 must be deposited every three months