In: Economics
Anna wants to have $5,000 saved when she graduates from college so that she will have a down payment for a new car. She already saved $300 dollars and her credit union pays 4% annual interest compounded monthly. How much money should she deposit each month to have the money available when she graduates in 3 years?
Step 1) Calculate the future value of the existing $300 after 3 year:
We are given the following information
Value of account at time 0 | PV | $ 300.00 |
rate of interest | r | 4.00% |
number of years | n | 3 |
Monthly Compounding | frequency | 12 |
Future value | FV | To be calculated |
We need to solve the following equation to arrive at the required FV
So the FV is $338.18
Step 2) Subtract the above calcualted FV from the required 5000 to calculate the balancing FV required to be accumulated from the monthly payments:
5000 - 338.18 = 4661.82
Step 3) Calculate the payment required to achieve the balancing FV:
We are given the following information:
Monthly payment | PMT | To be calculated |
rate of interest | r | 5.00% |
number of years | n | 3 |
Annual Compounding | T | 12 |
Balancing Future value | FV | $ 4,661.82 |
We need to solve the following equation to arrive at the required FV
So she needs to save 120.29 monthly