We need to find the amount of money that must be deposited at the beginning of each year for 3 years in an account that pays 7% interest, compounded annually, so that the account will contain $28,000 at the end of 3 years.

1. Problem Description

We need to find the amount of money that must be deposited at the beginning of each year for 3 years in an account that pays 7% interest, compounded annually, so that the account will contain $28,000 at the end of 3 years.

2. Solution Steps

Let $P$ be the amount deposited at the beginning of each year. Since the deposits are made at the beginning of each year, this is an annuity due. The formula for the future value of an annuity due is:

$FV = P \frac{(1+r)^n - 1}{r} (1+r)$

Where:

$FV$ = Future Value

$P$ = Periodic Payment (deposit)

$r$ = interest rate per period

$n$ = number of periods

In this problem:

$FV = 28000$

$r = 0.07$

$n = 3$

We need to solve for $P$:

$28000 = P \frac{(1+0.07)^3 - 1}{0.07} (1+0.07)$

$28000 = P \frac{(1.07)^3 - 1}{0.07} (1.07)$

$28000 = P \frac{1.225043 - 1}{0.07} (1.07)$

$28000 = P \frac{0.225043}{0.07} (1.07)$

$28000 = P (3.2149)(1.07)$

$28000 = P (3.439943)$

$P = \frac{28000}{3.439943}$

$P = 8140.907$

Rounding to the nearest cent, we get $P = 8140.91$.

3. Final Answer

$8140.91