Question

A sum of $250,000 earns interest at a rate of 12% per year compounded quarterly. How long
will it take for the investment to grow to $400,000?

Answer 1

Answer:

it will take 4 years.

Explanation:

The formula for this account is

   FV = 250000*(1+(0.12/4))*n,

where FV is the future value and "n" is the number of quarters.

So, you should solve this equation to find n

   400000 = 250000*0.13^n.

First, divide both sides by 250000.  You get

   400000/250000 = 1.03^n,   or

   1.6 = 1.03^n.

Next, take logarithm base 10 of both sides

   log(1.6) = n*log(1.03).

Hence,  n = log(1.6)/log(0.3) = 15.90 (rounded).

You want to find the number of quarters, which is an integer number.

Therefore, you round the value of 15.90 to the nearest greater integer, where next compounding will happen.

In this way, you get your

ANSWER.  16 quarters,  or 4 years.