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?
The problem with this question is that the interest period and the payment period does not match, so we can't use the standard formula
Secondly, you do not state if the 1.2% is a monthly rate or an annual rate compounded monthly. Seems pretty low for an annual rate, so I will assume it is a monthly rate.
- keep the payment period at weekly
- change 1.2% per month to a weekly rate.
let that weekly rate be i
(1+i)^52 = 1.012^12
1+i = 1.012^(12/52) = 1.0027565....
i = .0027565....
paym( 1.0027565....^260 - 1)/.0027565.... = 10,000
solve for paym, let me know what you get
To determine how much Mary should deposit at the end of each week to save $10,000 in 5 years, we need to break down the problem into smaller steps.
Step 1: Determine the interest rate per compounding period.
The interest rate is given as 1.2% per annum, compounded monthly. Since the interest is compounded monthly, we need to convert the annual interest rate to a monthly rate. To do this, we divide the annual interest rate by 12:
Monthly interest rate = 1.2% / 12 = 0.01
Step 2: Determine the number of compounding periods.
The money needs to be saved for 5 years, and since the interest is compounded monthly, the number of compounding periods is the number of years multiplied by 12:
Number of compounding periods = 5 years * 12 months/year = 60 months
Step 3: Use the formula for calculating compound interest.
The formula for calculating compound interest is:
Future value = Present value * (1 + interest rate)^number of periods
In this case, the future value is the desired amount of $10,000, the present value is the amount deposited each week, the interest rate is the monthly interest rate of 0.01, and the number of periods is 60 months.
Therefore, the formula becomes:
$10,000 = Deposit amount * (1 + 0.01)^60
Step 4: Solve for the deposit amount.
Rearrange the formula to solve for the deposit amount:
Deposit amount = $10,000 / (1 + 0.01)^60
Using a calculator or spreadsheet, calculate the deposit amount:
Deposit amount ≈ $10,000 / 1.795856
Deposit amount ≈ $5,569.93
Mary should deposit approximately $5,569.93 at the end of each week in a savings account to save $10,000 in 5 years for the future down payment on a car.