Question

A bank is negotiating a loan. The loan can either be paid off as a lump sum of $140,000 at the end of four years, or as equal annual payments at the end of each of the next four years. If the interest rate on the loan is 7%, what annual payments should be made so that both forms of payment are equivalent?

Answer 1

$27,000

Explanation:

8% interest rate on loan implies;

8/100 x $150,000 = $12,000

Making total payment at end of six years=

$12,000+ $150,000= $162,000

The annual payment now equals;

$162,000/6= $27,000

Note that the term annual payment means an equal amount of money to be paid yearly, which if summed up together would repay the loan amount when the repayment period ends

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Answer 2

Answer:

The annual payment is $31,531.93 to make both payments equivalent.

Step-by-step explanation:

The borrower has to repay the loan amount to the lender and he has two options to pay either by lump-sum payment or in installments. When the sum of periodic annual payment remains the same over the amortization period, it is an equal annual payment.

Calculation of equal annual payment:

Future value (FV) is $140,000.

Interest rate (r) is 7%.

Number of years (n) is 4.

Let annual equal payment be PMT.

$FV=PMT(\frac{1+r)^n - 1}{r} )$

$140000=PMT(\frac{1+0.07)^4 - 1}{0.07} )$

$140,000=$$PMT(\frac{1+0.07)^4 - 1}{0.07} )$

$PMT=\frac{140000}{4.439943}$

$PMT=31,531.93$

Hence, the annual payment is $31,531.93 to make both payments equivalent.

Reference Link

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