Question

an employee is paid twice a month. She has $100 withheld from each paycheck and invested in an annuity fund that averages 8.4% growth annually. She began when she turned 22.

(a) If she continues, how much will be in the fund when she turns 62?

(b) When she turns 62, how much of the value of the fund is interest earned?

Answer 1

ANSWER DOWN BELOW. FEEL FREE TO ASK ANY DOUBTS. THUMBS UP PLEASE.

Let's assume that there are 52 weeks in a year. Which means they are 26 bi weeks.

Rate = 8.4% p.a

Effective rate for a bi week= 8.4% /26 = 0.32307%

Formula: The Future Value of an ordinary annuity (FV)

FV= C× {[(1+r)^n]-1}/r

FV = Future value (The cumulative amount available in Future)

C= Periodic cash outflow. 100

r =effective interest rate for the period. 0.32307%

n = number of periods. (62-22)*26 =

FV= 100× {[(1+0.32307%)^1040]-1}/0.32307%

FV = $855,328.47

a. Fund available at age of 62 = $855,328.47

b. Interest earned = A- DEPOSITS MADE.

= $855,328.47- (1040*100)

= $751,328.47