Independent solution

How to solve this Staged Loan Payments question

Setup

Setup

Value the first five increasing payments separately as 100 times an increasing annuity-immediate. The remaining fifteen payments are level at X.

PV1:5=100(Ia)5‾∣ 0.05=1256.64PV_{1:5}=100(Ia)_{\overline5|\,0.05}=1256.64

Model

Model

At time 0, the level segment is X times a fifteen-payment annuity factor deferred five years. Add that to the first segment and equate to the 10,000 loan.

10000=1256.64+Xv5a15‾∣ 0.0510000=1256.64+Xv^5a_{\overline{15}|\,0.05}

Compute

Compute

The increasing segment is worth 1,256.64. Solving for the level payment gives X = 1,075.

X=1075X=1075

Answer

Answer

The calculation gives 1075 for staged loan payments, matching published choice E.

X=1075(E)\boxed{X=1075\quad\text{(E)}}