Independent solution

How to solve this Interest Rate Valuation question

Setup

Setup

Interest credited during a year equals the opening balance times the same two-half-year interest factor.

I12=100(1+i/2)22[(1+i/2)2−1]I_{12}=100(1+i/2)^{22}\left[(1+i/2)^2-1\right]

Model

Model

That common annual factor cancels from the ratio, leaving only balance growth between the starts of years five and twelve.

I5=100(1+i/2)8[(1+i/2)2−1]I_5=100(1+i/2)^8\left[(1+i/2)^2-1\right]

Compute

Compute

The balance exponents differ by 14 half-years, so the ratio condition determines the semiannual factor.

I12=2I5⟹(1+i/2)14=2I_{12}=2I_5\Longrightarrow(1+i/2)^{14}=2

Answer

Answer

Doubling the resulting half-year rate gives nominal annual rate 10.15%, choice A.

i=2(21/14−1)=10.15%(A)\boxed{i=2(2^{1/14}-1)=10.15\%\quad\text{(A)}}