the four people below have the following investments. invested amount interest rate compounding jerry $…
the four people below have the following investments. invested amount interest rate compounding jerry $ 12,100 12% quarterly elaine 15,100 6 semiannually george 22,100 8 annually kramer 18,100 10 annually required: 1-a. calculate the future value at the end of three years. (fv of $1, pv of $1, fva of $1, and pva of $1) 1-b. who has the greatest investment accumulation? complete this question by entering your answers in the tabs below. req 1a req 1b who has the greatest investment accumulation? who has the greatest investment accumulation?
Answer
Explanation:
Step1: Recall compound - interest formula
The formula for future value $FV = PV(1+\frac{r}{n})^{nt}$, where $PV$ is the present value, $r$ is the annual interest rate (in decimal), $n$ is the number of compounding periods per year, and $t$ is the number of years.
Step2: Calculate Jerry's future value
$PV = 12100$, $r=0.12$, $n = 4$ (quarter - ly compounding), $t = 3$. $FV_J=12100(1 +\frac{0.12}{4})^{4\times3}=12100(1 + 0.03)^{12}=12100\times1.425760886=17251.60$.
Step3: Calculate Elaine's future value
$PV = 15100$, $r = 0.06$, $n=2$ (semi - annual compounding), $t = 3$. $FV_E=15100(1+\frac{0.06}{2})^{2\times3}=15100(1 + 0.03)^{6}=15100\times1.194052297=18020.19$.
Step4: Calculate George's future value
$PV = 22100$, $r = 0.08$, $n = 1$ (annual compounding), $t = 3$. $FV_G=22100(1 + 0.08)^{3}=22100\times1.259712=27839.63$.
Step5: Calculate Kramer's future value
$PV = 18100$, $r = 0.10$, $n = 1$ (annual compounding), $t = 3$. $FV_K=18100(1 + 0.1)^{3}=18100\times1.331=24091.1$.
Step6: Compare future values
$FV_J=17251.60$, $FV_E=18020.19$, $FV_G=27839.63$, $FV_K=24091.1$.
Answer:
1 - a. Jerry: $$17251.60$, Elaine: $$18020.19$, George: $$27839.63$, Kramer: $$24091.1$ 1 - b. George