Question

2. An investor makes single deposits into a mutual fund of $250 in year 2 and $250 year 4, respectively. In addition, the investor starts making annual deposits starting at $500 in year 6, increasing the deposit by $100 annually in year 7 through year 10 (ending annual deposit would the fore be $900). What is the equivalent uniform annual amount of deposits over 10 years assuming a mutual fund ROR of 10%? Your solution will be closest to?

a. $175. b. $250   c. $320. d. $425

Answer 1

Let the deposits made in Year n be denoted by CFn

Given,
CF2 = 250
CF4 = 250
CF6 = 500
CF7 = 600
CF8 = 700
CF9 = 800
CF10 = 900

ROR = r = 10%

Present Value of deposits = ΣCFn/(1+r)ⁿ

= 250/(1+0.10)² + 250/(1+0.10)⁴ + 500/(1+0.10)⁶ + 600/(1+0.10)⁷ + 700/(1+0.10)⁸ + 800/(1+0.10)⁹ + 900/(1+0.10)¹⁰

= $1980.32

Let the uniform annual deposits be P

Number of years = n = 10

Present Value of uniform deposits = P/(1+r) + P/(1+r)² +....+ P/(1+r)ⁿ = P[1- (1+r)^-n]/r = P[1- (1+0.10)^-10]/0.10

This should be equal to the present value of the deposits calculated

=> 1980.32 = P[1- (1+0.10)^-10]/0.10

=> P = 1980.32*0.10/[1- (1+0.10)^-10] = $322.28 = $320 (rounded to nearest $5)

Hence, correct option is (c) $320