Question

A bank is negotiating a loan. The loan can either be paid off as a lump sum of $ 150 comma 000 at the end of six ​years, or as equal annual payments at the end of each of the next six years. If the interest rate on the loan is 8​%, what annual payments should be made so that both forms of payment are​ equivalent

Answer 1

Answer:

$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

Answer 2

Answer:

$20,447.31

Explanation:

we should use the annuity formula:

PMT = (FV x r) / [(1 + r)ⁿ - 1]

• FV = future value = $150,000
• r = interest rate = 8%
• n = number of periods = 6
• PMT = payment = ?

PMT = ($150,000 x 0.08) / [(1 + 0.08)⁶ - 1]

PMT = $12,000 / 0.5869 = $20,447.31

IF you pay 6 annual payments of $20,447.31, it should be equivalent to paying $150,000 in a lump sum.