Question

An investor deposits $50,000 in an account with Bank A that pays 12.5% interest compounded monthly.

Another investor deposits $50,000 in an account with Bank B that pays 12.4% interest compounded continuously. How much does each account have after 15 years?
Help me!!

Answer 1

To find the future values for both investments, we use the compound interest formula for monthly compounding for Bank A and the formula for continuous compounding for Bank B. The calculations provide the final amounts in each account after 15 years.

Step-by-step explanation:

Calculating Compound Interest

To calculate the future value of an investment with compound interest, we can use two different formulas based on how the interest is compounded. For the investor depositing $50,000 in Bank A with an interest rate of 12.5% compounded monthly, we use the formula:

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

Where:

• P = principal amount ($50,000)
• r = annual interest rate (0.125)
• n = number of times the interest is compounded per year (12)
• t = time the money is invested for (15 years)

After calculating, the future value for Bank A's account is found to be:

$50,000(1 + 0.125/12)^(12*15)

For the investor with Bank B with an interest rate of 12.4% compounded continuously, we use the formula for continuous compounding:

A = Pe^(rt)

After calculating, the future value for Bank B's account is:

$50,000e^(0.124*15)

Using these formulas will give us the final amounts in each account after 15 years.