Math 325
Problems – Ch 1 (1.1 – 1.8)
1. What is the present value of $1200 due in 8 years at an effective annual interest rate of 5.12%?
2. $10,250 accumulates to $23,237 in 13 years. What is the effective annual interest rate?
3. Ted borrowed an amount X today, and he plans to repay the loan with a payment of $1000 at the end
of 5 years and $2000 at the end of 7 years. If his loan has an annual effective rate of discount of 7%,
calculate X.
4.Tim deposits $10 into a fund today and $20 fifteen years later. Interest is credited at a nominal
discount rate d compounded quarterly for the first 10 years, and at a nominal interest rate of 6%
compounded semi-annually thereafter. The accumulated balance in the fund at the end of 30 years is
$100. Calculate d.
5. A deposit of X is made into a fund which pays an annual effective interest rate of 6% for 10 years.
At the same time, X/2 is deposited into another fund which pays an annual effective rate of discount d
for 10 years.
The amounts of interest earned over the 10 years are equal for both funds. Calculate d.
6. Investment X for 100,000 is invested at a nominal interest rate of j, convertible semiannually. After
four years, it accumulates to 214,358.88.
Investment Y for 100,000 is invested at a nominal rate of discount, k, convertible quarterly. After two
years, it accumulates to 232305.73.
Investment Z for 100,000 is invested at an annual effective rate of interest equal to j in one year, and an
annual effective rate of discount equal to k in year two.
Calculate the value of investment Z at the end of two years.