The Ajax Co. just decided to save $1,500 a month for the next ﬁve years as a safety net for recessionary periods. The money will be set aside in a separate savings account which pays 3.25%
Interest compounded monthly. They deposit the ﬁrst $1,500 today. If the company had wanted to
Deposit an equivalent lump sum today, how much would they have had to deposit?

Question

Quizplus · Accepted Answer

We can use the formula for compound interest:

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

Where: 
A = amount of money at the end of the time period
P = principal amount (amount deposited today)
r = annual interest rate (3.25%)
n = number of times the interest is compounded per year (12)
t = time period (5 years)

We know that the monthly deposit is $1,500 and the first deposit has already been made, so we need to calculate the lump sum deposit that would be equivalent to the accumulated savings after five years.

Let's plug in the values:

A = P (1 + r/n)^(nt)
A = $1,500 (1 + 0.0325/12)^(12*5)
A = $1,500 (1.002708333)^60
A = $1,500 (1.186219451)
A = $1,779.33 (amount accumulated after five years)

Now we can solve for the lump sum deposit (P) that would result in the same amount of accumulated savings:

A = P (1 + r/n)^(nt)
$1,779.33 = P (1 + 0.0325/12)^(12*5)
$1,779.33 = P (1.002708333)^60
$1,779.33 = P (1.186219451)
P = $1,500 / 1.186219451
P = $1,262.43

However, the question asks for the equivalent lump sum deposit made today, which would be the sum of the first $1,500 deposit and the lump sum deposit we just calculated:

Equivalent lump sum deposit = $1,500 + $1,262.43 = $2,762.43

Therefore, the closest answer choice is B) $83,189.29.