Independent solution

How to solve this Spot and Forward Rates question

Setup

Setup

Scale the loan amount to L; the level annual payment is determined at the contractual 10% rate.

R=La10‾∣0.10R=\frac{L}{a_{\overline{10}|0.10}}

Model

Model

At year 10, the first four payments have six additional years at 7%, while the last six form a 7% accumulated annuity.

F10=R[s4‾∣0.10(1.07)6+s6‾∣0.07]F_{10}=R\left[s_{\overline4|0.10}(1.07)^6+s_{\overline6|0.07}\right]

Compute

Compute

After cancelling L, the terminal-to-principal ratio is 2.29766883. Annualizing it over ten years gives yield 8.6748%.

(1+j)10=2.2976688285(1+j)^{10}=2.2976688285
j=0.08674773j=0.08674773

Answer

Answer

The bank's realized annual yield is approximately 8.67%, selecting choice D.

j≈8.67%(D)\boxed{j\approx8.67\%\quad\text{(D)}}