If the constant force of interest is 6%, what is the corresponding annual effective rate of interest?

1. (Problem 8.3) The amount of interest earned on A for one year is $562.50, while the equivalent amount of discount is $500. Find A.

2. (Problem 10.2) If the constant force of interest is 6%, what is the corresponding annual effective rate of interest?

3. (Problem 10.6) Bruce deposits 100 into a bank account. His account is credited interest at a nominal rate of interest of 4% convertible semiannually. At the same time, Peter deposits 100 into a separate account. Peter’s account is credited interest at a force of interest of δ. After 7.25 years, the value of each account is the same. Calculate δ.

4. (Problem 11.2) Find the accumulated value of 1 at the end of n years if the force of interest is δt = 1

1+t .

5. (Problem 11.9) Jennifer deposits 1000 into a bank account. The bank credits interest at a nominal annual rate of i compounded semi-annually for the first 7 years and a nominal annual rate of 2i convertible quarterly for all years thereafter. The accumulated amount in the account after 5 years is X. The accumulated amount in the account at the end of 10.5 years is 1,980. Calculate X.

6. (Problem 12.4) Brian and Jennifer each take out a loan of X. Jennifer will repay her loan by making one payment of 800 at the end of year 10. Brian will repay his loan by making one payment of 1,120 at the end of year 10. The nominal semi-annual rate being charged to Jennifer is exactly one-half the nominal semi-annual rate being charged to Brian. Calculate X.

7. (Problem 12.14) The parents of three children, ages 1, 3, and 6, wish to set up a trust fund that will pay X to each child upon attainment of age 18, and Y to each child upon attainment of age 21. They will establish the trust fund with a single investment of Z. Find the equation of value for Z.