the sanderses are saving up to go on a family vacation in 2 years. they invest $2300 into an account with an…
the sanderses are saving up to go on a family vacation in 2 years. they invest $2300 into an account with an annual interest rate of 1.11% compounded quarterly. answer the questions below. do not round any intermediate computations, and round your final answers to the nearest cent. if necessary, refer to the list of financial formulas. (a) assuming no withdrawals are made, how much money is in the sanderses account after 2 years? $ (b) how much interest is earned on the sanderses investment after 2 years? $
Answer
Explanation:
Step1: Identify the compound - interest formula
The compound - interest formula is $A = P(1+\frac{r}{n})^{nt}$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), $n$ is the number of times interest is compounded per year, and $t$ is the number of years.
Step2: Convert the given values to the appropriate form
We have $P=$2300$, $r = 1.11%=0.0111$, $n = 4$ (compounded quarterly), and $t = 2$ years.
Step3: Calculate the amount $A$
Substitute the values into the formula: [ \begin{align*} A&=2300\left(1 +\frac{0.0111}{4}\right)^{4\times2}\ &=2300\left(1+0.002775\right)^{8}\ &=2300\times(1.002775)^{8} \end{align*} ] Using a calculator, $(1.002775)^{8}\approx1.022477$. Then $A = 2300\times1.022477=$2351.6971\approx$2351.70$.
Step4: Calculate the interest earned
The interest earned $I$ is given by $I=A - P$. So $I=2351.70 - 2300=$51.70$.
Answer:
(a) $$2351.70$ (b) $$51.70$