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# interest rate, bond

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A zero coupon bond which will pay \$1,000 in ten years is selling today for \$422.41. What interest rate does the bond offer?

Lenny loanshark charges 1% per week on his loans. What APR must he report to consumers? Assume exactly 52 weeks in a year. What is the effective annual rate?

If you take out an 8,000 car loan that calls for 48 monthly payments at an APR of 10%, what is your monthly payment? What is the effective annual interest rate on the loan?

You want to buy a new car but you can only make an intital payment of only \$2,000 and can afford monthly payments of at most \$400. If the APR in auto loans is 12%and you finance the puchase over 48 months, what is the maximum price you can pay for the car?
How much can you afford if you finance it over 60 months?

In a discout interest loan, you pay the interest up front. For example if a 1-year loan is stated as \$10,000 and the interest rate is 10%, the borrower pays .10x\$10,000= \$1,000 immediatley, thereby receiving net funds of \$9,000 and repaying \$10,000 in a year.

a. What is the effective interest rate on this loan?
b. If you call the discount d (for example, d=10% using our numbers) express the effective annual rate on the loan as a function of d
C. Why is the effective annual rate always greater than the stated rate of d?

If you take out an 8,000 car loan that calls for 48 monthly payments of \$240 dollars what is the APR of the loan? Waht is the eeffective annual interst rate in the loan?

Reconsider the car loan in the previous question . Waht if the payments are made in 4 annual year end installments? Waht annual payment would have the same present value you calculated? Use the same effective annual interst rate as in the previous question. Why is your answer not simply 12 times the monthly payment?

A store offers two payment plans. Under the installment plan you pay 25% down and 25% f the purchase price in each of the next three years. If you pay the entire bill immediatley, you can take a 10% discount from the puchase price. Which is the better deal if you can borrow or lend funds at a 5% interest rate?

Reconsider the previous question. How will your answer change if the payments on the 4 year installment plan do not start for a full year?

If you borrow \$1,000 and agree to repay the loan in 5 equal annual payments at an interst rate of 12% what will you payment be? Waht if you make the first payment on the loan immediatley instead of at the end of the first year?

You've borrowed \$4,248.68 and agreed to pay back the loan with monthly payments of \$200. If the interest rate is 12% staed as an APR, how long will it take you to pay back the loan? What is the effective annual rate on the loan?

A retiree wants level consumption in real terms over a 30-year retirement. If the inflation rate equals the interest rate she earns on her \$450,000 of savings, how much can she spend in real terms over the rest of her life?

You invest \$1,000 at a 6% annual interst rate, stated as an APR. Interest is compounded monthly. How much will you have in 1 year? In 1.5 years?

You just borrowed \$10,000 to buy a condo. You will repay the loan in equal monthly payments of \$804.62 over the next 30 years. What monthly interest rate are you paying on the loan? What is the effective annual rate on the loan? What rate is the lender more likely to quote on the loan?

If a bank pays 6% interest with continuous compounding, what is the effective annual rate?

You buy a car that is advertised for \$12,000 on the following terms: (a) pay \$12,000 and receive a \$1,000 rebate from the manufacturer; (b) pay \$250 a month for 4 years for total payments of \$12,000, implying zero percent financing. Which is the better deal if the interest rate is 1% per month?