Question

an engineering graduate starts a new job at $68,000 per year. her investments are deposited at the end of the year into a mutual fund that earns a nominal interest rate of 5% per year with quarterly compounding. how much money will be in the account immediately after she makes the last deposit? (a)she makes $4000 annual deposits for the next 40 years.

Answer 1

To calculate the amount of money that will be in the account immediately after the last deposit, use the formula for compound interest. The final amount can be approximated to $471,452.48.

Step-by-step explanation:

To calculate the amount of money that will be in the account immediately after she makes the last deposit, we can use the formula for compound interest:

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

Where:

• A is the final amount
• P is the principal amount (the initial deposit)
• r is the annual interest rate (expressed as a decimal)
• n is the number of times the interest is compounded per year
• t is the number of years

In this case, the principal amount is $4000, the annual interest rate is 5% (or 0.05 as a decimal), the interest is compounded quarterly (so n = 4), and the number of years is 40.

Plugging in the values, we get:

A = 4000(1 + 0.05/4)^(4*40)

Using a calculator, we find that A ≈ $471,452.48