Question

over what period of time will money triple at 9% compounded quarterly

Answer 1

Let,

n= number of years.

P =initial amount.

A= future amount.

r=interest rate = 9%

According to the question , assume that value of P = x.

Then, value of A = 3.x

For compound interest, we have the formula,

A = P(1+r)n

Since it is compounded quarterly, new formula is

A = P(1+r/4)4n

Substituting the values,

3x = x(1 + 0.09/4)4n.

'x' get cancelled from both sides.

3 = 1(1+0.0225)4n.

= 1(1.0225)4n.

we need 'n',so taking log on each side.

log 3 = log (1.0225)4n

= 4n.log(1.0225).

4n =

4n = 49.37

then, n = = 12.34years

12.34 years is the required time period to triple the amount for this given condition.