Question

an investor buys a $25,000 (face value) 20-year bond that pays 4% annual interest with quarterly payments for $23,700. the investor sells the bond after six years for $22,850.

A.) What yearly rate of return did the investor realize on the investment ( show percent to two decimals)

B.) Give both the nominal yearly rate and the actual effective year

Answer 1

Copupon payment = 4% * 25000 / 4 = 250

t = 6*4 = 24 quarter

Let IRR per quarter be i%, then

250*(P/A,i%,24) + 22850*(P/F,i%,24) = 23700

Dividing by 50

5*(P/A,i%,24) + 457*(P/F,i%,24) = 474

using trail and error method

When i = 0.75%, value of 5*(P/A,i%,24) + 457*(P/F,i%,24) = 5*21.889146 + 457*0.835831 = 491.420682

When i = 1%, value of 5*(P/A,i%,24) + 457*(P/F,i%,24) = 5*21.243387 + 457*0.787566 = 466.134656

using intepolation

i= 0.75% + (491.420682-474)/(491.420682-466.134656)*(1%-0.75%)

i = 0.75% + 0.17% = 0.92% per quarter

Nominal return per year = 0.92%*4 = 3.68%

Effective return per year = (1+0.0092)^4 - 1 = (1.0092)^4 - 1 = 0.03731 ~ 3.73%