The James Co. plans on saving money to buy some new equipment. The company is opening an account today with a deposit of $15,000 and expects to earn 4% interest. After 3 years, the ﬁrm
Wants to add an additional $50,000 to the account. If the account continues to earn 4%, how much
Money will the James Co. have in their account ﬁve years from now?

Question

Quizplus · Accepted Answer

To solve this problem, we need to use the compound interest formula:

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

Where:
A = the amount of money in the account after t years
P = the initial deposit (or present value) 
r = the interest rate (as a decimal) 
n = the number of times the interest is compounded per year 
t = the time (in years)

In this problem:
P = $15,000 (initial deposit)
r = 0.04 (4% interest)
n = 1 (interest compounded annually)
t = 5 (total time)

We can use this formula to find the amount of money in the account after 3 years (when the company adds $50,000) and then continue to compound the interest for the remaining 2 years:

A1 = 15,000(1 + 0.04/1)^(1*3) = $17,717.44
A2 = (17,717.44 + 50,000)(1 + 0.04/1)^(1*2) = $72,329.79

Therefore, the James Co. will have $72,329.79 in their account five years from now.

The answer is D.