Question

Which investment results in the greatest total amount?

Investment A: $4,000 invested for 5 years compounded semiannually at 6%.
Investment B: $5,000 invested for 3 years compounded quarterly at 2.7%.
Find the total amount of investment A.
$ (Round to the nearest cent as needed.)

Answer 1

Explanation:

The formula to calculate the future value of an investment with compound interest is:

FV = PV * (1 + (r/n))^(n*t)

Where:

PV is the present value (the initial investment)

r is the annual interest rate

n is the number of compounding periods per year

t is the number of years

For Investment A:

PV = $4,000

r = 6% = 0.06

n = 2 (semiannual compounding)

t = 5 years

FV = $4,000 * (1 + (0.06/2))^(2*5) = $4,000 * (1.03)^10

FV = $4,000 * 1.664131669 = $6,656.53

So, the total amount of Investment A is $6,656.53 (rounded to the nearest cent).