a bank offers an investment account with an annual interest rate of 1.39% compounded annually. amanda…
a bank offers an investment account with an annual interest rate of 1.39% compounded annually. amanda invests $4100 into the account for 5 years. 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 amandas account after 5 years? (b) how much interest is earned on amandas investment after 5 years?
Answer
Explanation:
Step1: Identify compound - interest formula
The compound - interest formula when compounded annually is $A = P(1 + r)^t$, where $A$ is the amount of money in the account after $t$ years, $P$ is the principal amount (initial investment), $r$ is the annual interest rate (in decimal form), and $t$ is the number of years. Given $P=$4100$, $r = 0.0139$ (since $1.39%=0.0139$), and $t = 5$.
Step2: Calculate the amount in the account after 5 years
Substitute the values into the formula: $A=4100\times(1 + 0.0139)^5$. First, calculate $(1 + 0.0139)=1.0139$. Then, $(1.0139)^5=1.0139\times1.0139\times1.0139\times1.0139\times1.0139\approx1.071977$. Multiply by the principal: $A = 4100\times1.071977\approx4395.11$.
Step3: Calculate the interest earned
The interest earned $I$ is the difference between the final amount $A$ and the principal $P$. So, $I=A - P$. We know $A\approx4395.11$ and $P = 4100$. Then $I=4395.11-4100=295.11$.
Answer:
(a) $$4395.11$ (b) $$295.11$