Independent solution

How to solve this Equivalent Varying Accumulation question

Setup

Setup

Construct the accumulation under each of the two stated interest mechanisms over four years. One path is discrete; the other is the exponential of a varying-force integral.

10(1+K/25)4=10exp⁡(∫04dtK+0.25t)10(1+K/25)^4=10\exp\left(\int_0^4\frac{dt}{K+0.25t}\right)

Model

Model

Equating the two accumulation factors simplifies to 1 + 0.04K = (K + 1)/K. The positive admissible solution is K = 5.

(1+0.04K)4=((K+1)/K)4⟹K=5(1+0.04K)^4=((K+1)/K)^4\Longrightarrow K=5

Compute

Compute

With K fixed, the common accumulated value is 10(1.2)⁴ = 20.736, or 20.7.

A=10(1.2)4=20.736A=10(1.2)^4=20.736

Answer

Answer

The calculation gives 20.7 for equivalent varying accumulation, matching published choice A.

A=20.7(A)\boxed{A=20.7\quad\text{(A)}}