determine the amount of money that will be accumulated in an account that pays compound interest, given the…
determine the amount of money that will be accumulated in an account that pays compound interest, given the initial principal of $29,100 invested at 2.77% annual interest for 8 years compounded (a) daily (n = 365); (b) continuously. (a) $ will be accumulated in an account that pays interest that is compounded daily. (round to the nearest cent as needed.)
Answer
Explanation:
Step1: Recall compound - interest formula for daily compounding
The formula for compound interest 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. Given $P = 29100$, $r=0.0277$, $n = 365$, and $t = 8$. $A=29100(1 +\frac{0.0277}{365})^{365\times8}$
Step2: Calculate the value inside the parentheses first
$\frac{0.0277}{365}\approx0.00007589$. Then $1+\frac{0.0277}{365}=1 + 0.00007589=1.00007589$.
Step3: Calculate the exponent
$365\times8 = 2920$. So we have $(1.00007589)^{2920}$. Using a calculator, $(1.00007589)^{2920}\approx1.25097$.
Step4: Calculate the final amount
$A = 29100\times1.25097\approx36403.23$.
Answer:
$36403.23$