Question

1. Assume that you invest $3,249.66 and your investment grows at 9% for each of the first 2 years. At that point, you learn that the investment is likely to only earn 6% for the remaining 3 years. This means that you will not be able to reach your goal unless you invest more money. How much more would you have to deposit at the end of 2 years so that you can meet your goal? Round to two decimal points.

2. You are looking at investment that makes quarterly payments and has an expected return of 9%. If you would like to earn $500 per quarter for the next 6 years, how much do you need to invest today?

Answer 1

(1) Firstly we determine, the goal we might have reached if 9% growth rate continued for 5 years ( 2 + 3 years ).

Target amount = 3249.66 * ( 1.09)⁵ = 5000

Here we used, compound interest formula for a principal of 3249.66 with 9% interest rate ( equivalent to growth rate)

in n= 5 years.

But actual amount ............ Principal * ( 1 + r1)² * (1+r2)³

= 3249.66 * (1.09)² * (1.06)³

= 4598.42

Thus shortage in the target = 5000 - 4598.42 = 401.58

Additional amount to be deposited at the end of 2nd year = X

X * (1.06)³ = 401.58 .............Additional deposit must grow in 3 years to an amount = shortage of target.

X = 401.58 / (1.06)³

= 337.17

Question - 2

This present value of annuity model. We need an annuity of 500 per quarter, for 6 years * 4 = 24 payments at interest rate = 0.09/4 = 0.0225 per quarter.

Hence, amount to be deposited = present value of annuity = Annuity * [ 1 - (1+r)^-n ] / r  

= 500 * [ 1 - (1.0225)^-24 ] / 0.0225

= 9194.52