Question

An investment firm offers the​ following: Pay us ​$5033 per month for 141 ​months, and then we will pay you ​$5033 per month forever after that. What APY are they offering on this​ investment? ​ (In percent, rounded to 4​ decimals.)

Answer 1

Lets assume, Interest rate (monthly) = i

The Future value of monthly payment at the end of each of 141 months and Value of perpetual payment to be received must be same at interest rate(i).

Monthly payment (C) = $5033

Period (month) = 141

Future value (FV) of 141 payments -

putting the values -

And,

Perpetual payment (C) = $5,033

Interest rate = i

Value of Perpetual payment at end 141 months

And , FV = P

thus, Annual Percentage yield (APY) would be