Question

The compound interest formula is given by

A = P (1+r/n)ⁿᵗ
where is the accumulated amount, after an initial investment of dollars is invested for years, at annual interest rate , compounded times per year.
Use the formula above to determine the accumulated amount for each of the following different scenarios. Round solutions to the nearest cent. Assume there are 365 days in a year.

Scenario 1:
If 13,000 isinvested for 28 years and earns 5 interest, compounded semi-annually, the accumulated amount is:

Answer 1

For Scenario 1, with a $13,000 investment at a 5% annual interest rate, compounded semi-annually for 28 years, the accumulated amount would be $50,221.52. The compound interest earned in this scenario is $37,221.52.

Step-by-step explanation:

To calculate the accumulated amount using the compound interest formula A = P(1 + r/n)^(nt), we need to plug in the given values for the principal amount (P), the annual interest rate (r), the number of times the interest is compounded per year (n), and the number of years the money is invested (t).

For scenario 1, we have:

Using these values, the calculation is as follows:

A = 13000 * (1 + 0.05/2)^(2*28)

A = 13000 * (1 + 0.025)^(56)

A = 13000 * (1.025)^56

A = 13000 * 3.8631

A = $50,221.52

Therefore, the accumulated amount after 28 years is $50,221.52. To find the compound interest, subtract the original principal from this total:

Compound Interest = $50,221.52 - $13,000

Compound Interest = $37,221.52