Question

Mary wants to invest an amount every three months so that she will have $12,000 in three years to buy a new car. The account pays 2% compounded quarterly. How much should she deposit each quarter to have $12,000 after 12 deposits

Answer 1

Answer: $972.7972 or $973

To find the amount of money Mary should deposit each quarter, we will use the following equation:

$A=P\frac{((1+i)^n-1)}{i}$

Where:

P = deposit made n times

i = is the interest rate r compounded m times per year

Since Mary wants to invest every three months, that would be 4 times per year and have the interest rate of 2% = 0.02,

$i=\frac{0.02}{4}=0.005$

The amount she wants to save is A = $12000, and she will invest 12 times, n = 12.

Substituting these to the formula and we will have:

$12000=P\frac{(1+0.005)^{12}-1)}{0.005}$$12000=P\frac{((1.005)^{12}-1)}{0.005}$$P=\frac{12000(0.005)}{((1.005)^{12}-1)}$$P=\ 972.7972$

This means that Mary has to pay approximately $972.7972 or $973 each quarter.