Question

In: Finance

Suppose you borrow $20,000 at an annual rate of 6% and must repay it in 6...

Suppose you borrow $20,000 at an annual rate of 6% and must repay it in 6 equal installments at the end of each of the next 6 years. How much will you still owe at the end of the second year, after you make the second payment?

Solutions

Expert Solution

Answer:

Amount borrowed = $20,000

Annual rate = 6%

Payable in 6 equal installments at the end of each year

Annual payment = (P * R * (1+ R) ^N) / ((1+R)^N-1)

where:

P = Amount borrowed

R = Periodic Interest

N = number of installments

Annual payment = (20000 * 6% * (1 +6%) 6) / ((1 + 6%) 6 - 1)

= $4067.252569

This can also be calculated through excel formula PMT.

=PMT (6%, 6, -20000, 0, 0)

= $4067.252569

To get amount outstanding at the end of second year we have to calculate present value of remaining annual installments.

Number of remaining installments at the end 2nd year = 4

PV = Annual payment * (1 - 1 /(1 + interest rate) Number of years) / Interest rate

= 4067.252569 * (1 - 1 /(1 + 6%) 4) / 6%

= $14093.46

Alternately using excel, we get = PV (6%, 4, -4067.252569, 0,0) = $14093.45

Hence:

Amount you still owe at the end of the second year, after you make the second payment = $14,093.46


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