Question

A young couple needs $72,000 as a college fund for their two children. If they invest $52145 at 7.3% compounded semiannually. How long it would take to grow to $72,000?

The answer is 9 semiannual but I need help finding out how.

Answer 1

Let, P be the present amount of money

S be the amount after n years

r be the interest rate

m be the no. of compounding periods per year.

Then, we can write,

S = P * ( 1 + (r/m))mn

The money is compounded semiannually, i.e., money will be compounded twice a year.

So, let after n years the couple will be able to get 72000 $.

So, we can write,

52145 * (1 +(0.073/2))2*n = 72000

Or, (1 + 0.0365)2n = 1.38

Now, we take 'log' on both sides

2n * log(1.0365) = log(1.38)

Or, 2n =(log (1.38 )) / (log(1.0365))

Or, 2n = 8.98

Or, n = 4.49 ~ 4.5 years

If there are 2 compounding periods per year, then there will be 9 compounding periods in 4.5 years.