Question

Suppose you are invested in an (excellent) account that pays 50% interest per year, paid monthly. The account is closed to new investment, so you cannot reinvest the interest. Do you prefer this account to one that pays a single payment of 50% at the end of the year, rather than monthly? Why or why not? Explain your reasoning (you may wish to reference ideas like compounding, NPV, IRR, etc.)

Answer 1

ANSWER DOWN BELOW. FEEL FREE TO ASK ANY DOUBTS. THUMBS UP PLEASE.

Explanation:

It is better to invest in an account which pays interest monthly instead of in an account which pays interest annually.

Because we have the magic of compounding happening. Even though we cannot take out the monthly interest and reinvest it outside, still we are accumulating the interest in the same account. As it is accumulated in the same account we get its rate of interest.

In the below example: FV of Case 1 is greater than Case 2.

Which proves the above explanation.

Formula:
Future value= present value(1+r)^n

r= interest rate for the period.
n = number of periods.

Let PV = 1000

Case 1: paid monthly.

Future value= 1000(1+0.04167)^12
FV = 1632.09

r= interest rate for the period. (50%/12= 4.167% or 0.04167)
n = number of periods. (12)

Case 2: paid yearly

Future value= 1000(1+0.5)^1
FV = 1500

r= interest rate for the period. (50%= 0.5)
n = number of periods. (1)