Question

A company wants to have $240,000 available in 4 1/2 years for new construction. How much must be deposited at the beginning of each quarter (in $) to reach this goal if the investment earns 10.6% compounded quarterly?

Answer 1

To reach the goal of $240,000 in 4 1/2 years, approximately $167,881.84 must be deposited at the beginning of each quarter, considering an annual interest rate of 10.6% compounded quarterly.

Step-by-step explanation:

To calculate the amount that needs to be deposited at the beginning of each quarter, we can use the formula for compound interest:

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

Where:
A = the desired amount ($240,000)
P = the principal amount (to be determined)
r = the annual interest rate (10.6% or 0.106)
n = the number of times interest is compounded per year (4, since it is quarterly)
t = the number of years (4.5)

Substituting the given values into the formula:

$240,000 = P(1 + 0.106/4)^(4*4.5)

Solving for P, we get:

P = $240,000 / (1 + 0.0265)^(18)

P ≈ $167,881.84

Therefore, approximately $167,881.84 must be deposited at the beginning of each quarter to reach the goal of $240,000.