Question

Mary would like to save $10 000 at the end of 5 years for a future down payment on a car. 

an image of BMW's most recent concept car the GINA

a. How much should she deposit at the end of each month in a savings account that pays 1.2%/a, compounded monthly, to meet her goal?

b. If you currently have a part-time job, consider your hourly wage. If you do not have a job, use the minimum hourly wage in your jurisdiction. How many hours each month would you have to work, just to make those payments? Write a brief reflection on the advantages and disadvantages to long-term saving for a purchase, compared to borrowing a large sum of money and paying it off over time. Note that interest rates for savings accounts are always lower than interest rates for borrowing!

Answer 1

Please refer the image

a.

b.

Answer 2

Formula to determine the periodic deposit amount is

$$ P=\frac{A\left(\frac{r}{m}\right)}{\left[\left(1+\frac{r}{m}\right)^{m t}-1\right]} $$

Where, \(A\) is accumulated amount \(r\) is the compound interest rate \(m\) is the number of times compounded in annually and \(t\) is time in year.

Given that,

$$ \begin{aligned} &A=\$ 10,000 \\ &r=12 \%=0.12 \\ &t=5 \text { year } \\ &m=12(\text { monthly }) \\ &\Rightarrow P=\frac{10,000\left(\frac{0.12}{12}\right)}{\left[\left(1+\frac{0.12}{12}\right)^{(12)(5)}-1\right]}=122.44447 \end{aligned} $$

Since, she need to deposit each month \(\$ 122.44\) so, she should deposit at the end of each week is \(\frac{\$ 122.44}{30} * 7=\$ 28.57\)

Assume 1 month equals 30 days and 1 week equals 7 days.