Question

An annuity in perpetuity with effective annual interest rate i > 0 has present value $90. The annuity pays $30 at the end of each 5 year period, with the first payment at the end of year 10. Find i. please dont solve using excel

Answer 1

Annuity payment in each 5 year (P)= 30

Value of Perpetuity (PV)= 90

Periodical Interest rate of Perpetuity formula = P/PV

Periodical or 5 yearly rate = 30/90

=0.3333333333

(As Annuity is paid in 5 year, ínterest rate calculated from formula is matched as 5 year)

Effective 5 year period rate =0.3333333333

Number of yearly period in 5 year (m)= 5

Effective rate formula = ((1+yearly rate)^m)-1

0.3333333333=((1+I)^5)-1

1+0.3333333333= (1+I)^5

(1.333333333)^(1/5)= 1+I

1.059223841-1= I

I=0.05922384105 or 5.92%

So effective annual rate (I) is 5.92%