Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

A 4-year annuity of eight $9,800 semiannual payments will begin 7 years from now

ID: 2630911 • Letter: A

Question

A 4-year annuity of eight $9,800 semiannual payments will begin 7 years from now, with the first payment coming 7.5 years from now.

If the discount rate is 7 percent compounded monthly, what is the value of this annuity five years from now?

If the discount rate is 7 percent compounded monthly, what is the value three years from now?

If the discount rate is 7 percent compounded monthly, what is the current value of the annuity?

If the discount rate is 7 percent compounded monthly, what is the value of this annuity five years from now?

Explanation / Answer

The cash flows in this problem are semiannual, so we need the effective semiannual rate. The interest rate given is the APR, so the monthly interest rate is:

Monthly rate = 0.07 / 12 = 0.005833       

To get the semiannual interest rate, we can use the EAR equation, but instead of using 12 months as the exponent, we will use 6 months. The effective semiannual rate is:

Semiannual rate = (1.005833)6