Mary would like to save $10 000 at the end of 5 years for a future down payment on a car.How much should she deposit at the end of each week in a savings account that pays 1.2%/a, compounded monthly, to meet her goal?
To calculate the amount Mary should deposit at the end of each week, we need to use the formula for compound interest.
The formula for compound interest is:
A = P(1 + r/n)^(nt)
Where:
A is the future value (the amount Mary wants to save),
P is the principal (the amount Mary needs to deposit),
r is the annual interest rate (1.2%),
n is the number of times interest is compounded per year (monthly, so n = 12),
and t is the number of years (5).
We know that Mary wants to save $10,000, so A = $10,000.
We need to find P, the amount Mary needs to deposit.
Plugging in the values into the formula, we have:
$10,000 = P(1 + 0.012/12)^(12*5)
Simplifying:
$10,000 = P(1.001)^60
To isolate P, we divide both sides by (1.001)^60:
P = $10,000 / (1.001)^60
Using a calculator, we can compute the value of (1.001)^60:
(1.001)^60 ≈ 1.0734
Therefore, P ≈ $10,000 / 1.0734
P ≈ $9,313.09
Mary should deposit approximately $9,313.09 at the end of each week in a savings account to meet her goal of saving $10,000 at the end of 5 years.