Question

A 15-year annuity pays $1,475 per month, and payments are made at the end of each month. If the interest rate is 9 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.)

Answer 1

Step-by-step explanation:

First of all we shall calculate the present value of an annuity( at the end of 7 years ) of 1475

at interest rate of 6/12 = .5 % for total instalment of 12 x 8 = 96 ( 6% compounded monthly )

rate of intt .5% , no of instalment 96

PV of annuity of 1475

= 112252.66

This amount has to be discounted at 9 % to present value for 7 years

or calculated at 9/12 = .75% for 84 instalment

PV of 112252.66

= 59925.55

Now , we shall calculate PV of annuity of 1475 for 7 years compounted monthly ( rate of intt .75 % , no of instalment 84)

PV of annuity of 1475

= 91671.84

Total value

= 59925.55 + 91671.84

= 151597.39