Question

Suppose that $2000 is invested at a rate of 5.3%, compounded semiannually. Assuming that no withdrawals are made, find the total amount after 9 years.

Do not round any intermediate computations, and round your answer to the nearest cent.

Answer 1

Rounding to the nearest cent, the total amount after 9 years is $3182.67.

Explanation:

The formula for compound interest is given by:

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

where:

A = final amount

P = principal amount (initial investment)

r = annual interest rate (as a decimal)

n = number of times the interest is compounded per year

t = number of years

In this case, P = 2000, r = 0.053, n = 2 (compounded semiannually), and t = 9.

Plugging in these values, we get:

A = 2000(1 + 0.053/2)^(2*9)

= 2000(1.0265)^18

≈ 3182.67

Rounding to the nearest cent, the total amount after 9 years is $3182.67.