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

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Given:

P=Principal=218 cent=0.25 cent=0.0025 dollarsr=Annual interest rate=4%=0.04t=Time in years=2000 yearsm=Number of compounding periods per year=4(quarterly compounding)\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*}

Compound amount\textbf{Compound amount}

Formula for compound amount:

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

The interest rate per period ii is the annual interest rate rr divided by the number of compounding periods mm per year.

i=rm=0.044=0.01i=\frac{r}{m}=\frac{0.04}{4}=0.01

The number of compounding periods nn is the product of the number of compound periods mm per year and the time tt in years.

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

Evaluate the formula for the compound amount:

A=P(1+i)n=0.0025(1+0.01)8000Substitute=0.0025(1.01)8000Evaluate sum9,309,583,890,770,860,387,548,248,011,326Evaluate9.31×1031\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\$9,309,583,890,770,860,387,548,248,011,326.

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