Question

Sarah invests her graduation money of $1.750 in an annuity that pays an

Answer 1

We have been given that Sarah invests her graduation money of $1,750 in an annuity that pays an  interest rate of 6% compounded annually. We are asked to write an exponential function for her investment growth.

We will use compound interest formula to solve our given problem.

$A=P(1+\frac{r}{n})^{nt}$, where

A = Final amount after t years,

P = Principal amount,

r = Annual interest rate in decimal form,

n = Number of times interest is compounded per year,

t = Time in years.

$6\%=\frac{6}{100}=0.06$

Since interest is compounded annually, so $n=1$.

$f(t)=1750(1+\frac{0.06}{1})^{1\cdot t}$

$f(t)=1750(1+0.06)^{ t}$

$f(t)=1750(1.06)^{ t}$

Therefore, the function $f(t)=1750(1.06)^{ t}$ describes Sarah's investment growth.