Question

A 20-year annuity pays $1,450 per month, and payments are made at the end of each month. If the interest rate is 11 percent compounded monthly for the first ten years, and 7 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.)

Answer 1

- 20 year annuity pays $1450 per month at the end of each month.

Interest rate is 11% compounded monthly for the first ten years, and 7 percent compounded monthly in last 10 years.

calculating the Present Value at the end of year 10 of the last 10 years;-

Where, C= Periodic Payments = $1450

r = Periodic Interest rate = 7%/12 = 0.58333%

n= no of periods = 10 years*12 = 120

Present Value at the end of year 10 = $124,883.21

- SInce, in the first 10 years Interest rate is 11%, Calculating the Present Value today of first 10 years of annuity along with Present Value at the end of year 10:-

Where, C= Periodic Payments = $1450

r = Periodic Interest rate = 11%/12 = 0.91666%

n= no of periods = 10 years*12 = 120

PV10 = Present Value at the end of year 10 = $124,883.21

Present Value = $105,263.15 + $41,778.84

Present Value = $147,041.99

So, the present value of the annuity is $147,041.99