Question

11. Suppose you were hired on January 1, 2015 and started depositing $800 at the end of each quarter (meaning every three months, with the first deposit on March 31, 2015) in a pension fund that pays interest of 6% per year compounded quarterly on the minimum quarterly balance and credited at the end of each quarter.

(a.) How much money was in the pension fund on July 1, 2015?

(b.) How much money was in the pension fund of October 1, 2015?

(c.) How much money will be in the pension fund on January 1, 2045?

(d.) What is the total amount of interest earned in this pension fund during these 30 years?

Answer 1

(a)

Future value of fund on July 1, 2015 can be computed using formula for FV of annuity as:

FV = P x [(1 + r) n – 1/r]

P = Periodic Cash Deposit = $ 800

r = Periodic interest rate = 0.06/4 = 0.015 p. q.

n = Number of periods = 2

FV = $ 800 x [(1+ 0.015)2 – 1/r]

       = $ 800 x [(1.015)2 -1/0.015]

   = $ 800 x [(1.030225 -1)/0.015]

    = $ 800 x (0.030225 /0.015)

    = $ 800 x 2.015

    = $ 1,612

There will be $ 1,612 in the pension fund on July 1, 2015

(b)

Future value of fund on July 1, 2015 can be computed using same formula for FV of annuity.

n = 3 periods

FV = $ 800 x [(1+ 0.015)3 – 1/r]

       = $ 800 x [(1.015)3 -1/0.015]

   = $ 800 x [(1.045678375-1)/0.015]

    = $ 800 x (0.045678375/0.015)

    = $ 800 x 3.045225

    = $ 2,436.18

There will be $ 2,436.18 in the pension fund on October 1, 2015

(c)

Future value of fund on January 1, 2045 can be computed using same formula for FV of annuity.

n = 30 years x 4 periods = 120 periods

FV = $ 800 x [(1+ 0.015)120 – 1/r]

       = $ 800 x [(1.015)120 -1/0.015]

   = $ 800 x [(5.96932287232134-1)/0.015]

    = $ 800 x (4.96932287232134/0.015)

    = $ 800 x 331.288191488089

    = $ 265,030.553190471 or $ 265,030.55

There will be $ 265,030.55 in the pension fund on January 1, 2045

(d)

Interest earned = Total future amount – Total deposited amount

                           = $ 265,030.55 - $ 800 x 120

                           = $ 265,030.55 - $ 96,000

                           = $ 169,030.55

Total interest earned in the pension fund during 30 years is $ 169,030.55