What is the account value after 3 years?

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Question from Carlos, a student:

Hello,

I am working on the question below for a class.
I set up my formulas in Excel, but I get a different answer than the multiple choices.
My answer is $9,364.80
What am I doing wrong?

Question
Suppose that you deposited $3,000 at the beginning of each year for three years in a savings account earning 4%. What is the account value after 3 years (approx)?
a. 9,120
b. 9,211
c. 9,739
d. 9,989

My answer
Future Value of Regular Annuities
Payment $(3,000)
Years 3
Annual Rate 4%

Future Value $9,364.80

Your help is appreciated.

Regards,

Carlos

Hi Carlos,

You didn't say anything about compounding so I tried first with simple interest, that is no compounding at all.

First deposit after 3 years: $3,000(1 + 3 × 0.04)
Second deposit after 2 years: $3,000(1 + 2 × 0.04)
Third deposit after 1 years: $3,000(1 + 1 × 0.04)

Summing these three values gave me $9,720. Not very close to any of the multiple choice options.

I tried again with the interest being compounded once a year.

First deposit after 3 years: $3,000(1 + 0.04)³
Second deposit after 2 years: $3,000(1 + 0.04)²
Third deposit after 1 years: $3,000(1 + 0.04)

Summing these three values gave me $9,739.392 so I think the answer that is being sought is c.

Penny







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