We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.

+0

# Two Options

0
297
1

Objective: \$750,000 as a retirement plan. Rate 6% compounded annually.

Plan A: Deposit \$15,000 at the end of each year until objective reached.

Plan B: Deposit \$10,000 at the end of the first year, and an additional 5% over the previous year until objective reached. Question: which plan will get you there first and by how many years?

Any help will be appreciated. Thank you.

Aug 22, 2017

### 1+0 Answers

#1
0

Plan A is a simple, straightforward FV of \$1 per period, except here we need to solve for N in this formula:                                 FV=P{[1 + R]^N - 1/ R}
750,000 = 15,000 x {[1.06]^N - 1 / 0.06} divide both sides by 15,000
50 = {[1.06]^N -1 / 0.06}  cross multiply
3 = 1.06^N - 1 add 1 to both sides
4 = 1.06^N       take the log of both sides
N = Log(4) / Log(1.06)
N = 23.79 years to save \$750,000.

Plan B is a bit more involved, but there is a rarely-used formula for this type of investment, namely:
FV =P x {(1.05^N) - (1.06^N)} / (0.05 - 0.06)
750,000 = 10,000 x {(1.05^N) - (1.06^N)} / (0.05 -0.06) divide by 10,000
75 ={(1.05^N) - (1.06^N)} / (-0.01) cross multiply
-0.75 ={(1.05^N) - (1.06^N)}
As far as I know, there is no direct solution for N. Somebody should correct me on this. But, by simple iteration we get:
N = 23.0244 years to save \$750,000

As you can see the two plans are quite similar. Plan B being slightly faster at getting to your objective of \$750,000. The difference being:
23.79 - 23.0244 =0.7656 years - or about 9.2 months faster.

Aug 23, 2017