Rui Baldwin

2021-09-07

The amount owed at the end of 5 years.
An amount of $\mathrm{}3000$ is loaned at a rate of $10\mathrm{%}$compounded quarterly.

Clara Reese

Step 1
Formula used:
The compound interest formula, $A=P{\left(1+\frac{r}{n}\right)}^{nt}$
Here A is the amount after t years,
P is the principal amount,
r is the annual interest rate and n is number of periods the interest compounding.
Step 2
To find the amount owed at the end of 5 years, we will substitute in the above compound interest formula and solve for A. Since the interest rate is compounded quarterly, so we substitute $n=4$. So, we get
$A=P{\left(1+\frac{r}{n}\right)}^{nt}$
$=3000{\left(1+\frac{0.1}{4}\right)}^{4×5}$
$=3000{\left(1+0.025\right)}^{20}$
$=3000{\left(1.025\right)}^{20}$
$\approx \mathrm{}4915.85$
Thus, the amount owed is approximately $\mathrm{}4915.85$ at the end of 5 years.

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