MATH SOLVE

8 months ago

Q:
# please helpSam deposits $12,500 each year into a retirement account with a 3% simple interestrate. If he deposits the same amount each year, how much money will he have at theend of his fourth year?$13,625 $26,725 $52,250$54,500

Accepted Solution

A:

Answer:$53750Step-by-step explanation:Sam deposit $12500 every year which grows at a simple interest of 3% and we have to calculate the total sum after 4 years.
If Sam deposit $x with r% simple interest then the principal will grow after 4 years to [tex]x[1 + \frac{4r}{100}][/tex]
Again, for the second year $x investment with r% simple interest will grow to [tex]x[1 + \frac{3r}{100}][/tex].
Now, the third year $x investment with r% simple interest will grow to [tex]x[1 + \frac{2r}{100}][/tex]
And finally the fourth year $x investment with r% simple interest will grow to [tex]x[1 + \frac{r}{100}][/tex]
Therefore, the total sum becomes
[tex]x[1 + \frac{4r}{100}] + x[1 + \frac{3r}{100}] + x[1 + \frac{2r}{100}] + x[1 + \frac{r}{100}][/tex]
= [tex]4x + \frac{10 \times r \times x}{100}[/tex]
= [tex]4x + \frac{rx}{10}[/tex]
So, in case of Sam the sum will be = [tex]4 \times 12500 + \frac{3 \times 12500}{10}[/tex] = $53750