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# Valuing Delayed Annuities; Amortizing Loan;Interest rate ris

34. Valuing Delayed Annuities. Suppose that you will receive annual payments of \$10,000 for a
period of 10 years. The first payment will be made 4 years from now. If the interest rate is 5
percent, what is the present value of this stream of payments?

36. Amortizing Loan. You take out a 30-year \$100,000 mortgage loan with an APR of 6 percent
and monthly payments. In 12 years you decide to sell your house and pay off the mortgage.
What is the principal balance on the loan?

29. Annuity Value. Your landscaping company can lease a truck for \$8,000 a year (paid at yearend)
for 6 years. It can instead buy the truck for \$40,000. The truck will be valueless after 6
years. If the interest rate your company can earn on its funds is 7 percent, is it cheaper to buy
or lease?

28. Interest Rate Risk. Suppose interest rates increase from 8 percent to 9 percent. Which bond
will suffer the greater percentage decline in price: a 30-year bond paying annual coupons of 8
percent, or a 30-year zero coupon bond? Can you explain intuitively why the zero exhibits
greater interest rate risk even though it has the same maturity as the coupon bond?

#### Solution Preview

34. In this case you should find the PVIFA for 14 years and for 4 years. Subtract the 4 year value from the 14 year value to get the PVIFA to 10 years with a 4 year delay. PVIFA for 14 years at 5% is 9.899 and for 4 years and 5% is 3.546. For 10 years with a delay of 4 years is 9.899-3.546=6.353. The Present Value is ...

#### Solution Summary

The solution has various problems relating to annuties and interest rate risk

\$2.19