#### Question

In the New Testament, Jesus commends a widow who contributed 2 mites to the temple treasury (Mark 12:42-44). A mite was worth roughly 1/8 of a cent. Suppose the temple invested those 2 mites at 4% interest compounded quarterly. How much would the money be worth 2000 years later?

#### Solution

Verified#### Step 1

1 of 2Given:

$\begin{align*} P&=\text{Principal}=2\cdot \frac{1}{8}\text{ cent}=0.25\text{ cent}=0.0025\text{ dollars} \\ r&=\text{Annual interest rate}=4\%=0.04 \\ t&=\text{Time in years}=2000\text{ years} \\ m&=\text{Number of compounding periods per year}=4&\color{#4257b2}(\text{quarterly compounding}) \end{align*}$

$\textbf{Compound amount}$

Formula for compound amount:

$A=P(1+i)^n$

The interest rate per period $i$ is the annual interest rate $r$ divided by the number of compounding periods $m$ per year.

$i=\frac{r}{m}=\frac{0.04}{4}=0.01$

The number of compounding periods $n$ is the product of the number of compound periods $m$ per year and the time $t$ in years.

$n=mt=4(2000)=8000$

Evaluate the formula for the compound amount:

$\begin{align*} A&=P(1+i)^n \\ &=0.0025\left(1+0.01\right)^{8000} &\color{#4257b2}\text{Substitute} \\ &=0.0025\left(1.01\right)^{8000} &\color{#4257b2}\text{Evaluate sum} \\ &\approx 9,309,583,890,770,860,387,548,248,011,326 &\color{#4257b2}\text{Evaluate} \\ &\color{#4257b2}\approx 9.31\times 10^{31} \end{align*}$

Thus the compound amount is $\$9,309,583,890,770,860,387,548,248,011,326$.