A 15-year annuity pays $1,650 per month, and payments are made at the end of eac

Question

A 15-year annuity pays $1,650 per month, and payments are made at the end of each month. If the interest rate is 10 percent compounded monthly for the first seven years, and 6 percent compounded monthly thereafter, what is the present value of the annuity? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

A 15-year annuity pays $1,650 per month, and payments are made at the end of each month. If the interest rate is 10 percent compounded monthly for the first seven years, and 6 percent compounded monthly thereafter, what is the present value of the annuity? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Explanation / Answer

First compute the last 8 years present value at the end of 7 years.

Rate = 6%/12 = 0.5%.

Payment (Pmt) = 1650.

Nper = 8*12 = 96 months.

Compute the present value using excel function.

PV = PV(Rate,Nper,Pmt,FV) = PV(0.5%,96,-1650,0) = $125,557.11.

Therefore, the present value of the cash flows for eight years after the end of year 7 is $125,557.11.

Thus, it is termed as Future value and the future value = $125,557.11.

Rate = 10%/12 = 0.0833%.

Nper = 7* 12 = 84 months.

Compute the present vlaue using excel function.

PV =PV(Rate,Nper,Pmt,FV) = PV(10%/12,84,1650,125557.11) = $161921.43.

Therefore, the present vlaue of the annuity is $161,921.43.

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