Question

Use the present value formula to determine the amount to be invested now, or the present value needed.

The desired accumulated amount is $140,000 after 2 years invested in an account with 8% interest compounded quarterly.

The amount to be invested now, or the present value needed, is $ ____
(Round to the nearest cent as needed.)

Answer 1

The value needed now is $102,296.60

Explanation:

Here, we want to calculate the present value needed.

We shall be using the formula for compound interest here

Mathematically;

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

According to the question;

I is the initial amount which is what we want to calculate

A is the accumulated amount with interest = 140,000

r is the interest rate = 8% = 8/100 = 0.08

n is the number of times interest is compounded which is 4, since it is quarterly

t is the number of years = 2

Substituting these values, we have ;

140,000 = I(1 + 0.08/2)^(4 * 2)

140,000 = I(1.04)^8

I = 140,000/(1.04)^8

I = 102,296.62870027774

Which is I = $102,296.60 to the nearest cent