question 13, 4.c.59 part 1 of 4 consider the two savings plans below. compare the balances in each plan…

question 13, 4.c.59 part 1 of 4 consider the two savings plans below. compare the balances in each plan after 10 years. which person deposited more money in the plan? which of the two investment strategies is better? yolanda deposits $200 per month in an account with an apr of 6%, while zach deposits $2000 at the end of each year in an account with an apr of 6.5%. the balance in yolandas saving plan after 10 years was $ (round the final answer to the nearest cent as needed. round all intermediate values to seven decimal places as needed.)

question 13, 4.c.59 part 1 of 4 consider the two savings plans below. compare the balances in each plan after 10 years. which person deposited more money in the plan? which of the two investment strategies is better? yolanda deposits $200 per month in an account with an apr of 6%, while zach deposits $2000 at the end of each year in an account with an apr of 6.5%. the balance in yolandas saving plan after 10 years was $ (round the final answer to the nearest cent as needed. round all intermediate values to seven decimal places as needed.)

Answer

Explanation:

Step1: Identify the formula for future - value of an ordinary annuity

The formula for the future - value of an ordinary annuity is $F = A\times\frac{(1 + r)^{n}-1}{r}$, where $A$ is the amount of each payment, $r$ is the interest rate per period, and $n$ is the number of periods. For Yolanda: The annual percentage rate (APR) is $6%=0.06$. The monthly interest rate $r=\frac{0.06}{12}=0.005$. The number of years is $t = 10$ years, and the number of monthly payments $n=10\times12 = 120$. The monthly payment $A = 200$.

Step2: Calculate the future - value of Yolanda's annuity

Substitute the values into the formula: [ \begin{align*} F&=200\times\frac{(1 + 0.005)^{120}-1}{0.005}\ &=200\times\frac{(1.005)^{120}-1}{0.005} \end{align*} ] First, calculate $(1.005)^{120}$. Using the formula $a^{b}$, where $a = 1.005$ and $b = 120$, we have $(1.005)^{120}\approx1.819396734$. Then, $(1.005)^{120}-1\approx1.819396734 - 1=0.819396734$. $\frac{(1.005)^{120}-1}{0.005}=\frac{0.819396734}{0.005}=163.8793468$. $F = 200\times163.8793468=32775.87$

Answer:

$32775.87$