Question

You have just purchased an increasing annuity-immediate for 75,000 that makes twenty annual payments as follows:
(a) 5P, 10P, . . . , 50P during years 1 through 10, and
(b) 50P(1.05), 50P(1.05)^2 , . . . , 50P(1.05)^10 during years 11 through year 20.
The annual effective interest rate is 7% for the first 10 years and 5%, thereafter. Solve for P.
P=175.29 I need to know how to get this cause I can't figure it out

Answer 1

Since given that we have purchased the annuity at t=0 for 75,000

Therefore the present value of the annuity at the discount rate of annual effective rate will be equal to 75,000.

As we can see two things here, First - P is common in all in all years , Second - from 11 years & onwards the Numerator and denominator on mathematical operation giving us the value of 10th year annuity

Therefore the updated equation will be

Solving this equation, we get

75000 = P x ( 427.8703)

Which gives us , P = 175.2868