Question

What sum of money received is equivalent to $150,000 received at the end of six years from now if the current interest rate is annually 6% compounded every four months period? Write the name of the equation used to solve and explain.

Answer 1

Solution : if the interest rate is compounded every four month then we have to multiply the year with number of compounding period to find out in 6 year time how much time it has been compounded.

Here total compounding period = 4 * 6 = 24

And the interest rate of one compounding period will be = i/4 = r = 0.06/4 = 0.015

Now let us use our formula of future value

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

present value is x suppose

150000 = x (1+0.015)^24

150000/1.015^24 =x

x = 104931.58

So the value of x = 104931.58 if compounded for four months for six years will give us an amount equal to 150000

let us check

FV = 104931.58(1+0.015)^25 = 150000