Question

What would be the nominal rate of interest compounded quarterly for an $135,000 annuity to pay you $1,400 at the end of every three months for 30 years.

Answer 1

Quarterly Payment = 1400

Number of quarter = 30*4 = 120

PV = 135000

PV = Sum of present value of all the quarterly payment discounted at quarterly rate

135000 = 1400/(1+quarterly rate)^1 + 1400/(1+quarterly rate)^2 + 1400/(1+quarterly rate)^3 + 1400/(1+quarterly rate)^4 + 1400/(1+quarterly rate)^5 + 1400/(1+quarterly rate)^6 + 1400/(1+quarterly rate)^7 + 1400/(1+quarterly rate)^8 + .................... 1400/(1+quarterly rate)^119 + 1400/(1+quarterly rate)^120

We will use heat and trial method to get that value for which above equation satisfy.

I/Y = Quarterly Rate = 0.38

Nominal rate of interest = 0.375*4 = 1.5% Answer

Or Using Financial Calculator:

PV = 135000

PMT = -1400

N = 120

FV = 0

CPT -> I/Y

I/Y = Quarterly Rate = 0.38

Nominal rate of interest = 0.375*4 = 1.5% Answer

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