Question

Andrew invested $5000 in an account that earns 3.8% interest, compounded annually. The formula for compound interest is

`A(t)=P(1+i)^{t}`



How much did Matthew have in the account after 3 years?

Answer 1

To calculate how much Matthew has in his account after 3 years with the given compound interest formula, we need to identify the variables in the formula:

- \( P \) = principal amount (initial investment) = $5000
- \( i \) = interest rate (as a decimal) = 3.8% = 0.038
- \( t \) = number of years = 3

The formula for compound interest is:

\[
A(t) = P(1 + i)^{t}
\]

Now we can substitute the values into the formula:

\[
A(3) = 5000(1 + 0.038)^{3}
\]

First, calculate \( 1 + 0.038 \):

\[
1 + 0.038 = 1.038
\]

Now raise that to the power of 3:

\[
(1.038)^{3} \approx 1.117
\]

Next, multiply that by the principal amount:

\[
A(3) = 5000 \times 1.117 \approx 5585
\]

Therefore, after 3 years, Matthew will have approximately:

\[
\boxed{5585}
\]