Question

I’m 28 now, and let’s say I want to set up a sinking fund that will be worth $300,000 when I retire at age65. I plan to make monthly payments to an annuity with 6% interest. How much should those payments be? What’s my contribution? How much interest do I earn?

Answer 1

Monthly payment = $ 184

Total contribution = $ 81,696

Interest earned = $ 218,304

Explanation:

Periodic deposit can be computed by using formula for FV of annuity as:

FV = P x [(1+r) ⁿ -1/r]

P = FV/[(1+r) ⁿ -1/r]

P = Periodic deposit

FV = Future value of fund = $ 300,000

r = Rate of interest = 0.06/12 = 0.005 p.m.

n = Number of periods = (65 -28) years x 12 months = 37 x 12 = 444

P = $ 300,000/ [(1+0.005)⁴⁴⁴ – 1/0.005]

= $ 300,000/ [(1.005)⁴⁴⁴ – 1/0.005]

= $ 300,000/ [(9.15654048374506 -1)/0.005]

= $ 300,000/ (8.15654048374506 /0.005)

= $ 300,000/1631.30809674901

= $ 183.901496349992 or $ 184

Monthly payment = $ 184

Total contribution = Monthly payment x Number of payments = $ 184 x 444 = $ 81,696

Interest earned = FV - Total contribution = $ 300,000 - $ 81,696 = $ 218,304