Suppose you want to have $700,000 for retirement in 25 years. Your account earns 7% interest.
a) How much would you need to deposit in the account each month?
b) How much interest will you earn?
To calculate the monthly deposit and interest earned, we can use the formula for future value of an ordinary annuity:
FV = P * (((1 + r)^n - 1) / r)
Where:
FV = Future value (desired amount)
P = Monthly deposit
r = Monthly interest rate
n = Number of months
a) To find the monthly deposit, we rearrange the formula to solve for P. Let's plug in the given values:
FV = $700,000
r = 7% per year = 7%/12 per month
n = 25 years * 12 months = 300 months
700,000 = P * (((1 + (7%/12))^300 - 1) / (7%/12))
We need to solve this equation for P. However, it's a complex equation to solve manually. Hence, we can use an online financial calculator or spreadsheet software like Microsoft Excel to find the monthly deposit.
b) To calculate the interest earned, we can subtract the total amount deposited from the final value:
Interest = FV - (P * n)
Using the same values:
Interest = 700,000 - (P * 300)
Once we find the monthly deposit amount (using a calculator or spreadsheet), we can substitute that value to calculate the interest earned.