Question

Calvin took out a loan for college for

$25,000. If the interest rate is 4%
annually, what is the total amount of
money Calvin will owe after 4 years?

Answer 1

`~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+(r)/(n)\right)^(nt) \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$25000\\ r=rate\to 4\%\to (4)/(100)\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &4 \end{cases} \\\\\\ A = 25000\left(1+(0.04)/(1)\right)^(1\cdot 4) \implies A=25000(1.04)^4\implies A \approx 29246.46`

Answer 2

$29,246.5

Explanation:

Original amount: $25,000

If the interest rate is 4%, let's change that into decimal form, so move the decimal point two places two the left, giving us a rate of 0.04

We can multiply 25,000 by 0.04 to see how much money he owes for the first year, giving us 1,000

Now, including the 25,000 original amount plus the 1,000 Calvin owes after the first year, we have 26,000 TOTAL that he owes. We can multiply that by 0.04 to find how much he owes after the 2nd year,and so on until we get to the 4th year.

So, from the beginning:

year 1- 25000 x 0.04 = 1000 + 25000 = 26000

year 2- 26000 x 0.04 = 1040 + 26000 = 27040

year 3- 27040 x 0.04 = 1081.6 + 27040 = 28121.6

year 4- 28121.6 x 0.04 = 1124.9 + 28121.6 = 29246.5