## Felipe deposited S4000 into an account with 5.8% interest, compounded semiannually. Assuming that no withdrawals are made, how much will he

Question

Felipe deposited S4000 into an account with 5.8% interest, compounded semiannually. Assuming that no withdrawals are made, how much will he have in the
account after 8 years?
Do not round any intermediate computations, and round your answer to the nearest cent.

in progress 0
2 weeks 2021-09-08T20:52:27+00:00 2 Answers 0

1. Answer: he would have \$6319.8 after 8 years.

Step-by-step explanation:

We would apply the formula for determining compound interest which is expressed as

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

Where

A = total amount in the account at the end of t years

r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount deposited

From the information given,

P = \$4000

r = 5.8% = 5.8/100 = 0.058

n = 2 because it was compounded twice in a year.

t = 8 years

Therefore,

A = 4000(1 + 0.058/2)^2 × 8

A = 4000(1 + 0.029)^16

A = 4000(1.029)^16

A = \$6319.8

Amount in the account after eight years = \$9858.95

Step-by-step explanation:

Compound interest is given by:

Where:

A = final amount

P = Initial Balance

r = Rate of interest

n = number of time periods elapsed

Here, P = 4000; r = 5.8/100;

n:

For every year, the interest is compounded twice (semiannually).

Hence, for eight years, there are 16 time periods.

n = 16.

A = 4000*[(1+0.058)^16] = 9858.95\$