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Sam has $50 in an account that earns 5% interest compounded annually.

To the nearest cent, how much will he have in 3 years?

2 Answers

3 votes

Final answer:

Sam will have approximately $57.88 in his account after 3 years with 5% compound interest compounded annually on his initial $50.

Step-by-step explanation:

The question is asking us to calculate the future value of $50 with 5% compound interest compounded annually over 3 years. To find out the amount Sam will have after 3 years, we can use the compound interest formula: A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial sum of money), r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years.

In Sam's case, P = $50, r = 0.05 (5%), n=1 (since it is compounded annually), and t = 3 years. Plugging in these values,

the formula becomes:

A = $50(1 + 0.05/1)^(1*3)

This simplifies to:

A = $50(1.05)^3

After calculation, we find that the total future amount that Sam will have after 3 years to the nearest cent is approximately:

A = $50(1.157625) = $57.88

User Adam Fletcher
by
8.5k points
14 votes

Answer:

$57.50

Step-by-step explanation:

50×5/100×3

=7.5

50+7.5

=57.50

User Neeraj Joshi
by
8.9k points

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