An investor’s retirement account pays an annual nominal interest rate of 4.2%, convertible monthly. On January 1 of year y, the investor’s account balance was X. The investor then deposited 100 at the end of every quarter. On May 1 of year (y + 10), the account balance was 1.9X.

Determine which of the following is an equation of value that can be used to solve for X.

• [[math]]\frac{1.9X}{\left(1.0105\right)^{\frac{124}{3}}}+\sum_{k=1}^{42}\frac{100}{\left(1.0105\right)^{k-1}}=X [[/math]]
• [[math]]X+\sum_{k=1}^{42}{\frac{100}{(1.0035)^{3(k-1)}}}={\frac{1.9X}{(1.0035)^{124}}} [[/math]]
• [[math]]X+\sum_{k=1}^{41}\frac{100}{(1.0035)^{3k}}=\frac{1.9X}{(1.0035)^{124}}[[/math]]
• [[math]]X+\sum_{k=1}^{41}{\frac{100}{(1.0105)^{k-1}}}={\frac{1.9X}{(1.01105)^{\frac{124}{3}}}} [[/math]]
• [[math]]X+\sum_{k=1}^{42}{\frac{100}{(1.0105)^{k-1}}}={\frac{1.9X}{(1.0105)^{\frac{124}{3}}}}[[/math]]

Five deposits of 100 are made into a fund at two-year intervals with the first deposit at the beginning of the first year. The fund earns interest at an annual effective rate of 4% during the first six years and at an annual effective rate of 5% thereafter.

Calculate the annual effective yield rate earned over the investment period ending at the end of the tenth year.

• 4.18%
• 4.40%
• 4.50%
• 4.58%
• 4.78%

Jack inherited a perpetuity-due, with annual payments of 15,000. He immediately exchanged the perpetuity for a 25-year annuity-due having the same present value. The annuity-due has annual payments of X. All the present values are based on an annual effective interest rate of 10% for the first 10 years and 8% thereafter.

Calculate X.

• 16,942
• 17,384
• 17,434
• 17,520
• 18,989

An insurance company purchases a perpetuity-due providing a geometric series of quarterly payments for a price of 100,000 based on an annual effective interest rate of i. The first and second quarterly payments are 2000 and 2010, respectively.

Calculate i.

• 10.0%
• 10.2%
• 10.4%
• 10.6%
• 10.8%

A perpetuity provides for continuous payments. The annual rate of payment at time t is

Using an annual effective interest rate of 6%, the present value at time t = 0 of this perpetuity is x.

Calculate x.

• 27.03
• 30.29
• 34.83
• 38.64
• 42.41

Martha leaves an estate of 500,000. Interest on this estate is paid to John for the first X years at the end of each year. Karen receives annual interest payments from the end of year X+1 forever. At an annual effective interest rate of 5%, the present value of Karen’s interest payments is 1.59 times the present value of John’s.

Calculate X.

• 6
• 7
• 8
• 9
• 10

Which of the following is an expression for the present value of a perpetuity with annual payments of 1, 2, 3, ..., where the first payment will be made at the end of n years, using an annual effective interest rate of i?

• [[math]]\frac{\ddot{a}_{\overline{n}|}-nv^n}{i}[[/math]]
• [[math]]\frac{n-a_{\overline{n}|}}{i}[[/math]]
• [[math]]\frac{v^n}{d}[[/math]]
• [[math]]\frac{v^n}{d^2}[[/math]]
• [[math]]\frac{v^n}{di}[[/math]]

For a given interest rate i > 0, the present value of a 20-year continuous annuity of one dollar per year is equal to 1.5 times the present value of a 10-year continuous annuity of one dollar per year.

Calculate the accumulated value of a 7-year continuous annuity of one dollar per year.

• 5.36
• 5.55
• 8.70
• 9.01
• 9.33

An annuity having n payments of 1 has a present value of X. The first payment is made at the end of three years and the remaining payments are made at seven-year intervals thereafter.

Determine X.

• [[math]]\frac{a_{\overline{7n+3}|} - a_{\overline{3}|}}{s_{\overline{3}|}}[[/math]]
• [[math]]\frac{a_{\overline{7n+3}|}-a_{\overline{3}|}}{a_{\overline{7}|}}[[/math]]
• [[math]]\frac{a_{\overline{7n+3}|}-a_{\overline{7}|}}{a_{\overline{3}|}}[[/math]]
• [[math]]\frac{a_{\overline{7n+3}|}-a_{\overline{7}|}}{a_{\overline{7}|}}[[/math]]
• [[math]]\frac{a_{\overline{7n+3}|}-a_{\overline{7}|}}{s_{\overline{3}|}}[[/math]]

At an annual effective interest rate of 10.9%, each of the following are equal to X:

• The accumulated value at the end of n years of an n-year annuity-immediate paying 21.80 per year.
• The present value of a perpetuity-immediate paying 19,208 at the end of each n-year period.

Calculate X.

• 1555
• 1750
• 1960
• 2174
• There is not enough information given to calculate X