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


Related Solutions

6. Suppose you borrow $50,000 at a rate of 5% compounded annually and must repay it...
6. Suppose you borrow $50,000 at a rate of 5% compounded annually and must repay it in 5 equal installments at the end of each of the next 5 years. a. How much will your first installment be? b. How much will you still owe after you pay your first installment?
If you borrow $20,000, you have to repay in equal instalments over four years. Interest Rate...
If you borrow $20,000, you have to repay in equal instalments over four years. Interest Rate is 9%. What is the interest payment in the fourth year, 14. a) 1499 b)1171 c)510 d)977 e)1406 f)814
You borrow $42,000 and repay the loan with 6 equal annual payments. The first payment occurs...
You borrow $42,000 and repay the loan with 6 equal annual payments. The first payment occurs one year after receipt of the $42,000 and you pay 8% annual compound interest. a)Solve for the payment size. b)What is the payment size when interest is 8% compounded monthly, and monthly payments are made over 6 years? c)What is the payment size when interest is 8% compounded semiannually, and annual payments are made over 6 years? d)What is the payment size when the...
Suppose you borrowed $50,000 at a rate of 8.5% and must repay it in5 equal...
Suppose you borrowed $50,000 at a rate of 8.5% and must repay it in 5 equal installments at the end of each of the next 5 years. By how much would you reduce the amount you owe in the first year?
Suppose you borrowed $50,000 at a rate of 8.5% and must repay it in 5 equal...
Suppose you borrowed $50,000 at a rate of 8.5% and must repay it in 5 equal installments at the end of each of the next 5 years. By how much would you reduce the amount you own in the first year?
upon graduating school you must repay $20,000 in student loans your interest rate is 6.8% how...
upon graduating school you must repay $20,000 in student loans your interest rate is 6.8% how much will your payment be if you make monthly payments over the standard 10 year payment term
You borrowed $45,000 at 4% annual interest rate that you must repay over 3 years. The...
You borrowed $45,000 at 4% annual interest rate that you must repay over 3 years. The loan is amortized into three-equal end-of-year payments.         (a) Calculate annual payment amount         (b) Prepare a loan amortization schedule         (c) If you make equal monthly payment for 36 months, calculate monthly payment amount and prepare a monthly loan amortization schedule        (d) How much is total interest charge for 3 years, if you make annual payment? How much is total interest charge...
Suppose Shin borrowed $70,000 on a student loan at a rate of 10% and must repay...
Suppose Shin borrowed $70,000 on a student loan at a rate of 10% and must repay it in 5 equal installments at the end of each of the next 5 years. a. Construct an amortization schedule. b. What is the annual interest expense for the borrower and the annual interest income for the lender during Year 4?
You borrow $90,000 to buy 2019 Tesla Model S, the annual interest rate is 6% and...
You borrow $90,000 to buy 2019 Tesla Model S, the annual interest rate is 6% and you have 5 years to pay off your loan with monthly payments. After 2 years you want to refinance the loan, how much do you still owe on the car? $54,371.73 $57,193.99 $62,295.11 $24,888.99 At a family gathering, your uncle hears that you are taking a finance course with many real life applications. He wants to consult you regarding a new house he likes...
Your sibling wants to borrow money from you that she can repay in four equal annual...
Your sibling wants to borrow money from you that she can repay in four equal annual payments of $1,000 at the end of each of the next four years. If you charge 3% interest rate on the loan to your sibling, and that is the competitive interest rate, what would be the amount that you can lend to her today? Group of answer choices $ 3,717.10 $ 3,828.61 $ 3,956.72 $ 4,310.13 $ 3,,549.95 $ 3,289.55
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT