Question

9. Mr. Richards has a new client will earn much higher returns than normal because of their risk profile. The client will role $75,000 into an account with the firm and then they will make additional monthly deposits of $2,000 per month for the next 25 years. He also wants to illustrate the returns for a bank CD at 2%, market returns at 4% and normal returns for him of 8%. To further illustrate the power of his returns, he wants to show the returns at 12% for 20 years.

Excel: Use the standard TVM setup. Remember M is 12 for monthly. Setup a summary table showing the rates and overall portfolio value and one additional 20-year return. Also show the overall growth rates as in the previous analysis.

Written: Briefly describe the analysis that you have performed and explain the effect of compound interest. Explain how the compound interest and growth rates differ across the different returns. Provide 3 summary points to sell this client for Mr. Richards.

Answer 1

One time investment = $75000

Monthly deposit for 25 yrs = $2000

Corpus built

Scenario 1

rate @ 2%

PV = 75000 (One time)

rate (r) = 2%

tenure (n) = 25

PVA = 2000 (annuity)

rate (r) = 2% / 12 = 0.17%

tenure (n) = 25*12 = 300

FVIF formula = (1+r)^n

FVIFA formula = [(1+r)^n]-1] / r

Future Value of Investment = 75,000 * FVIF (2%, 25) + 2000 * FVIFA (0.17%, 300)

= 75,000 * ((1+0.02)^25) + 2000 * [(1+0.0017)^300]-1] / 0.0017

= 1,23,045.45 + 7,81,847.31 = 9,04,892.76

Scenario 2

market returns r = 4%

Future Value of Investment = 75,000 * FVIF (4%, 25) + 2000 * FVIFA (0.33%, 300)

= 75,000 * ((1+0.04)^25) + 2000 * (((1+0.0033)^300)-1)/0.0033

= 1,99,937.72 + 10,22,334.28 = 12,22,272

Scenario 3

normal returns = 8%

Future Value of Investment = 75,000 * FVIF (8%, 25) + 2000 * FVIFA (0.67%, 300)

= 75,000 * ((1+0.08)^25) + 2000 * (((1+0.0067)^300)-1)/0.0067

= 5,13,635.64 + 19,14,463.45 = 24,28,099.45

Scenario 4

r = 12%, n = 20 (for one time investment)

r = 1%; n = 20 * 12 = 240

Future Value of Investment = 75,000 * FVIF (12%, 20) + 2000 * FVIFA (1%, 240)

= 75,000 * ((1+0.12)^20) + 2000 * (((1+0.01)^240)-1)/0.01

= 7,23,471.98 + 5,13,635.64 = 27,01,982.71

Summary of corpus built for various rates / tenure -

One time amount $75,000 and annuity of $2000 monthly for the mentioned tenure -

Points to sell -

1.Compound interest is considered the eighth wonder of the world

2. The importance of achieving higher returns at any given level of risk is pertinent as can be seen in scenario 4 where the corpus built is higher than the other scenarios despite having a lower tenure

3. The magic of compound interest lies in consistent investment and higher returns. Also, most of the corpus accumulates over the long haul.