Problem: Calculate the value of your retirement if you contribute $5000 today, $1000 at the end of each year, at 8% interest for 30 years. Repeat the same question with 14%.
To calculate the value of your retirement savings, you need to use a financial formula called the future value of an ordinary annuity.
The formula to calculate the future value of an ordinary annuity is:
FV = P * ((1 + r)^n - 1) / r
Where:
FV = Future Value
P = Payment (annuity amount)
r = Interest rate per period
n = Number of periods
Let's solve the problem step by step:
At 8% interest:
1. Calculate the future value of the initial contribution of $5000:
Using the formula with P = 5000, r = 8% (0.08), and n = 30, we have:
FV = 5000 * ((1 + 0.08)^30 - 1) / 0.08
2. Calculate the future value of the annual contributions of $1000:
Using the formula with P = 1000, r = 8% (0.08), and n = 30, we have:
FV = 1000 * ((1 + 0.08)^30 - 1) / 0.08
3. Add the future values of the initial contribution and the annual contributions to get the total future value of your retirement savings.
Repeat the same calculation with an interest rate of 14% using the same steps and formula, but with r = 14% (0.14) instead.
By following these steps, you should be able to calculate the value of your retirement savings under different interest rates.