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 find out how much Mary should deposit at the end of each week, we need to consider the compounding frequency and the interest rate.

Step 1: Convert the annual interest rate to the monthly interest rate.
The annual interest rate is 1.2%. To convert it to a monthly rate, divide it by 12 (the number of months in a year).
Monthly interest rate = 1.2% / 12 = 0.1% = 0.001

Step 2: Calculate the number of weeks in 5 years.
Since Mary wants to save for 5 years, we need to know how many weeks are in 5 years. There are 52 weeks in a year, so multiply 52 by 5.
Number of weeks in 5 years = 52 * 5 = 260 weeks

Step 3: Calculate the future value of the savings.
We can use the future value formula for monthly compounding to calculate the amount Mary needs to deposit each week:

FV = P * (1 + r)^n
Where:
FV = Future Value (the goal of $10,000)
P = Principal (the amount Mary needs to deposit)
r = interest rate per period (monthly interest rate of 0.001)
n = number of periods (260 weeks)

Rearranging the formula to solve for P:
P = FV / (1 + r)^n

Plugging in the values:
P = $10,000 / (1 + 0.001)^260
P = $10,000 / (1.001)^260

Step 4: Use a calculator or spreadsheet to calculate the value of P.
Using a calculator or spreadsheet, evaluate the expression (1.001)^260 and divide $10,000 by the result to find the amount Mary should deposit each week.

P ≈ $8.66

Therefore, Mary should deposit approximately $8.66 at the end of each week in a savings account to reach her goal of saving $10,000 in 5 years, given a 1.2% annual interest rate compounded monthly.