Question

To ensure that funds are available to repay the principal at maturity, a borrower deposits $2000 each year for three years. If interest is 6% compounded quarterly, how much will the borrower have on deposit four years after the first deposit was made?

Answer 1

The borrower will have approximately $8,167.20 on deposit after four years.

Step-by-step explanation:

To calculate the amount the borrower will have on deposit after four years, we can use the formula for compound interest:

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

Where:

• A is the final amount on deposit
• P is the annual deposit
• r is the interest rate (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 annual deposit is $2000, the interest rate is 6% (or 0.06), the interest is compounded quarterly (so n = 4), and the number of years is 4 (since the first deposit was made 4 years ago).

Plugging in these values, we get:

A = 2000(1 + 0.06/4)^(4*4)

A ≈ $8,167.20