Questions: Margo borrows 200, agreeing to pay it back with 5% annual interest after 10 months. How much interest will she pay? Round your answer to the nearest cent, if necessary. Find the balance if 28000 is invested in an account paying 8.5% interest compounded quarterly for 6 years. The balance will be How much would you need to deposit in an account now in order to have 4000 in the account in 15 years? Assume the account earns 3% interest compounded monthly.

Solution Steps

Margo borrows \( \$200 \) at an annual interest rate of \( 5\% \) for \( 10 \) months. The interest can be calculated using the formula: \[ \text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time} \] Converting \( 10 \) months to years gives \( \frac{10}{12} = \frac{5}{6} \) years. Thus, the interest is: \[ \text{Interest} = 200 \times 0.05 \times \frac{5}{6} = 8.33 \] So, Margo will pay \( \$8.33 \) in interest.

If \( \$28,000 \) is invested at an annual interest rate of \( 8.5\% \) compounded quarterly for \( 6 \) years, the balance can be calculated using the compound interest formula: \[ A = P \left(1 + \frac{r}{n}\right)^{nt} \] where \( P = 28000 \), \( r = 0.085 \), \( n = 4 \), and \( t = 6 \). Thus, the balance is: \[ A = 28000 \left(1 + \frac{0.085}{4}\right)^{4 \times 6} \approx 46379.67 \] The balance after \( 6 \) years will be \( \$46,379.67 \).

To find out how much needs to be deposited now to have \( \$4,000 \) in \( 15 \) years at an interest rate of \( 3\% \) compounded monthly, we use the present value formula: \[ P = \frac{A}{\left(1 + \frac{r}{n}\right)^{nt}} \] where \( A = 4000 \), \( r = 0.03 \), \( n = 12 \), and \( t = 15 \). Thus, the present value is: \[ P = \frac{4000}{\left(1 + \frac{0.03}{12}\right)^{12 \times 15}} \approx 2551.95 \] Therefore, you would need to deposit \( \$2,551.95 \) now.

Final Answer