Independent solution

How to solve this Annuities and Perpetuities question

Setup

Setup

The first payment occurs at month 60 and the last at month 240, giving 181 payments.

P=∑k=0180750(1.01)k(1.006)60+kP=\sum_{k=0}^{180}\frac{750(1.01)^k}{(1.006)^{60+k}}

Model

Model

Factor out the first-payment discount and recognize the remaining terms as a finite geometric series.

P=750(1.006)60∑k=0180(1.011.006)kP=\frac{750}{(1.006)^{60}}\sum_{k=0}^{180}\left(\frac{1.01}{1.006}\right)^k

Compute

Compute

The monthly payment growth exceeds the monthly yield, but the series remains finite and evaluates to about 138,440.

P=138440P=138440

Answer

Answer

The annuity present value is 138,440, corresponding to choice C.

P≈138440(C)\boxed{P\approx138440\quad\text{(C)}}