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(((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=(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((1+0.005)^(12)-1))/(0.005)`
`12000=P(((1.005)^(12)-1))/(0.005)`
`P=(12000(0.005))/(((1.005)^(12)-1))`
`P=\$972.7972`

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