Independent solution

How to solve this Loan Amortization question

Setup

Setup

Use a monthly effective rate of 0.5% and value all payments at loan issue.

im=0.06/12=0.005i_m=0.06/12=0.005

Model

Model

Each block is an annuity-immediate because payments occur at month-end.

10000=Pa30‾∣+1.1Pv30a40‾∣+1.2Pv70a50‾∣10000=Pa_{\overline{30}|}+1.1Pv^{30}a_{\overline{40}|}+1.2Pv^{70}a_{\overline{50}|}

Compute

Compute

The later blocks require deferrals equal to the number of months before each block starts.

P=10000a30‾∣+1.1v30a40‾∣+1.2v70a50‾∣P=\frac{10000}{a_{\overline{30}|}+1.1v^{30}a_{\overline{40}|}+1.2v^{70}a_{\overline{50}|}}

Answer

Answer

Only choice E uses immediate timing and deferrals of 30 and 70 months.

equation in choice E\boxed{\text{equation in choice E}}