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Alina [70]
3 years ago
14

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
Business
1 answer:
MaRussiya [10]3 years ago
3 0

Answer:

A) $24,602

Explanation:

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

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

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 = (1+\frac{r}{m}) ^m-1

where; r = 12.5% = 0.125

(1+\frac{0.125}{12})^{12} -1

= 0.1324

Interest rate per period = \frac{0.1324}{4}

= 0.0331

Then;

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

220,000 = PMT × 8.986

PMT = \frac{220,000}{8.986}

PMT = $ 24,482.5

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

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

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