Independent solution

How to solve this Geometrically Increasing Deposits question

Setup

Setup

Let A be each monthly deposit during year 1 and let j = 0.002 be the monthly rate.

j=0.024/12=0.002j=0.024/12=0.002

Model

Model

For year k from zero through nine, twelve beginning-of-month deposits have amount A times 1.1 to the k. Accumulate every deposit to month 120.

21,234.05=A∑k=09∑m=0111.1k(1.002)120−(12k+m)21{,}234.05=A\sum_{k=0}^{9}\sum_{m=0}^{11}1.1^k(1.002)^{120-(12k+m)}

Compute

Compute

The double-sum coefficient is 212.340609, so A is 99.99995. The fifth-year amount applies four annual increases.

A=99.99995A=99.99995
K=A(1.1)4=146.4099K=A(1.1)^4=146.4099

Answer

Answer

The fifth-year monthly deposit is 146.41, choice C.

K=146.41(C)\boxed{K=146.41\quad\text{(C)}}