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 12%/a, compounded monthly, to meet her goal?
d. Determine the weekly deposit without technology.
Can someone provide me with the formula please?
That is called a sinking fund
Since it is compounded monthly do it all monthly and divide the deposit by 4 to get the weekly figure.
S =D [ (1+r)^n -1 ] /r
S is what we need at the end, in this case 10,000
D is the monthly deposit (remember divide it by four for weekly)
n is the number of compounding periods, in this case 5*12 = 60
r is the interest rate (decimal) at each compounding period, in this case .12/12 = .01
so
10,000 = D[ 1.01)^60 -1 ] / .01
10,000 = D (0.817)/.01 = D (81.7)
D = 122.44
D/4 = $30.61 per week
Sure! The formula to calculate the weekly deposit without using technology is:
Weekly Deposit = Future Value / Present Value Factor
In this case, we need to find the Present Value Factor for a monthly compounding period at a 12% annual interest rate for 5 years. The Present Value Factor is calculated using the formula:
Present Value Factor = 1 / (1 + (Interest Rate / number of compounding periods))^(number of compounding periods * number of years)
For monthly compounding, we have 12 compounding periods per year. Let's calculate the Present Value Factor:
Present Value Factor = 1 / (1 + (0.12 / 12))^(12 * 5)
Present Value Factor = 1 / (1 + 0.01)^(60)
Present Value Factor = 1 / (1.01)^(60)
Present Value Factor ≈ 0.564
Now, we can use the formula for the weekly deposit:
Weekly Deposit = $10,000 / 0.564
Weekly Deposit ≈ $17,730.50
Therefore, Mary should deposit approximately $17,730.50 at the end of each week to save $10,000 at the end of 5 years for a future down payment on a car.
The formula to calculate the weekly deposit without the use of technology to meet a future savings goal is as follows:
Weekly Deposit = (Future Value - Initial Deposit) / (Number of Weeks)
In this case, Mary wants to save $10,000 at the end of 5 years. To calculate the future value, we need to use the compound interest formula:
Future Value = Principal * (1 + (Interest Rate / Number of Compoundings))^(Number of Compoundings * Number of Years)
Let's break down the information provided:
Principal (Initial Deposit) = 0 (Since Mary hasn't made any deposit yet)
Future Value = $10,000
Interest Rate = 12% per year
Number of Compoundings = 12 (since the interest is compounded monthly)
Number of Years = 5
Now, we can substitute these values into the formula to calculate the future value:
Future Value = (0) * (1 + (0.12 / 12))^(12 * 5)
Future Value = 0 * (1 + 0.01)^(60)
Future Value = 0 * (1.01)^(60)
Future Value = 0
Based on the calculation, the future value is currently $0 since no initial deposit has been made.
Now, we can plug in the values into the formula to calculate the weekly deposit:
Weekly Deposit = ($10,000 - $0) / (Number of Weeks)
Since Mary wants to save for 5 years, which consists of 52 weeks per year, the number of weeks would be:
Number of Weeks = Number of Years * Number of Weeks per Year
Number of Weeks = 5 * 52
Number of Weeks = 260
Plugging in the values, we can calculate the weekly deposit:
Weekly Deposit = ($10,000 - $0) / 260
Weekly Deposit = $10,000 / 260
Weekly Deposit = $38.46 (rounded to two decimal places)
So, without using technology, Mary would need to deposit approximately $38.46 at the end of each week in a savings account to meet her goal of $10,000 in 5 years.