Problem solving: You are an investor and you need to choose among the three options which is better off. To elaborate further you need to show all the details below:

Question

You are an investor and there are three options for investing ¥50,000. The first earns 8%

compounded semi-annually, the second earns 8% compounded monthly, and the third earns

8% compounded annually.

1. Construct the model and which investment yields the highest return after 20 years. What is the difference in earnings between each investment?
2. How long would it take to have an amount of ¥150,000 with an interest rate of 5% compounded monthly ? Show your solution

Answer 1

The equation for calculating compounding interest is shown below:

A = P(1+r/n)^nt

A = final amount

P = initial principle balance

r = interest rate

n = number of times interest is applied per time period

t = number of time periods passed

For this situation:

A = 50000(1+0.08/n)^n*20

semi-annually: A = 50000(1+0.08/2)^2*20 = ¥240051

monthly: A = 50000(1+0.08/12)^12*20 = ¥246340

annually: A = 50000(1+0.08/1)^1*20 = ¥233047

Clearly monthly interest is the best option.

To find the time to reach ¥150000, we will set up the equation and solve for t using logarithms.

150000 = 50000(1+0.05/12)^12*t

3 = (1+0.05/12)^12*t

log(3) = log((1+0.05/12)^12*t)

log(3) = 12*t*log(1+0.05/12)

t = log(3)/12log(1+0.05/12)

t = 22 years