Question

A man is offered two proposals to invest his money. The first offer is to invest $ 20,000 in the bank for 10 years with 9% compounded annually for the next 5 years and 10% compounded annually thereafter. The second offer is to purchase a $ 17,000 with 12% bond maturing in 10 years which is offered for 20,000. Which proposal should he choose? and why?

Note: Please write the steps.

Answer 1

We have to calculate the future value in both the scenarios

At first, amount to be invested in both the cases is same $20,000. So, this figure is non relevant for decision making as the same amount is going as outflow in both the cases

Future value = Present value x (1 + r) ^ n

Where,

Present value = Amount invested = $20,000 in case 1 and $17,000 in case 2

r = Rate of interest = 9% and 10% in case 1 and 12% in case 2

n = Number of period of investment = 10 years

Case 1

Future value when interest rate is different in a particular period

= Present value x (1 + r1)^n1 x (1 + r2) ^ n2

= $20,000 x 1.09^5 x 1.10^5

= $20,000 x 1.538623 x 1.61051

= $49,559.38

Case 2

Future value

= $17,000 x 1.12^10

= $17,000 x 3.105848

= $ 52,799.41

So, as we can find from the above calculations, the future value is more in case 2 than in case 1. So, Case 2 or Proposal 2 should be selected