Question

How Much Capital Do You Need to Start Investing? The motivation for making investments is largely driven by the goals you have. These goals could be short-term such as buying a new car, saving for a down payment or save enough to take a year off and travel. In any situation, the first step is to identifying the amount of capital you need and how much risk are you willing to take for the return you expect. Larry is a 25-year-old dietician whose primary long-term financial goal is to save enough to take a year off and travel. Therefore, he wants to begin an investment plan that will make this a reality within 5 years. He currently has $3,000 saved for this purpose, and he wants to determine the appropriate monthly savings amount that will allow him to reach his goal. He estimates that he can earn an average annual return of 5%, and he would like to save a total of $20,000 to cover his expenses for the year. Table of Future Value Factors Table of Future Value Annuity Factors Year 1 5 10 40 2% 1.020 1.104 1.219 2.208 5% 1.050 1.276 1.629 7.040 8% 1.080 1.469 2.159 21.724 10% 1.100 1.611 2.594 45.258 Year 1 5 10 40 2% 1.000 5.204 10.950 60.401 5% 1.000 5.526 12.578 120.797 8% 1.000 5.867 14.487 259.052 10% 1.000 6.105 15.937 442.580 If he invests the $3,000 today, the terminal value of this initial investment in 5 years (earning an average 5% return) will be . This means that he must accumulate the remaining| through his annual savings plan to obtain the full $20,000 to cover his expenses for the year. Still assuming an average return on investment of 5%, the additional yearly investment required to reach Larry's targeted financial goal within 5 years is

Answer 1

Solution

If he invests $ 3000, the terminal value of this investment in 5 years @5% would be = $3,000 x (1+0.05)⁵ = 3000 x 1.05⁵ = 3000 x 1.276 = $ 3,828

(Future value of $1 @5% after 5 years is 1.276 from the future value table)

This means he must accumulate the remaining = $20,000 - $ 3828 = $ 16,172 through annual savings to obtain the full amount to cover his expenses for one year.

The additional yearly investment to reach his targeted financial goal within 5 years is $ 2,926.53 which is explained below:

Formula to find future value of annuity is FVA = A x [(1+r)ⁿ - 1] $\div$ r

where FVA = future value of annuity; A = annuity (his annual saving, assumed to be fixed); r = annual rate of return; n = tenure of investment

We need to find A given the other values.

So, 16,172 = A x [1.05⁵ - 1] $\div$ 0.05

A = 16,172 $\div$ { [(1+0.05)⁵ - 1] $\div$ 0.05 } …...(i)

From the future value of annuity table above this value of [(1+0.05)⁵ - 1] $\div$ 0.05 which is the future value of annuity of $1 for 5 years is given as 5.526.

Hence in the above equation (i) we have A = 16,172 $\div$ 5.526 = 2,926.53.

If he had no capital saved and needed to accumulate the entire $ 20,000 in next 5 yrs his annual contribution would have to be $ 3,619.25

This is because the above equation (i) now becomes A = $ 20,000 $\div$ { [(1+0.05)⁵ - 1] $\div$ 0.05 } = 20,000 $\div$ 5.526 = $ 3,619.25

When he starts with initial investment of $ 3,000 total amount he ends up contributing to accumulate $ 20,000 is equal to the initial investment plus additional yearly payments totalling $ 3000 + ($ 2,926.53 x 5) = $ 17,632.65

When he starts with no initial capital contribution he accumulates $ 3,619.25 x 5 = $ 18,096.25

The answer to the last question is False since the investment plan would not only depend on the total amount he intends to save (since that would affect the required rate of return from the investment plan) but also the investment objective (since that may affect the timing of repayment of capital and return as well as the rate of return). For instance, if he would not require the entire amount for his expenses at a point in time after the 5th year but in fixed monthly instalments over the 6th year, an annuity plan with fixed contribution per annum may be more suitable than 4 or 5 CDs created over 5 years.