You need to have $50,000 at the end of 10 years. To accumulate this sum, you have decided to save a certain amount at the end of each of the next 10 years and deposit it in the bank. The bank pays 8 percent interest compounded annually for long-term deposits. How much will you have to save each year (to the nearest dollar)?
Just use your future value formula
P*(1.08^10-1)/0.08 = 50000
Now solve for P
Plz explain this question
To determine how much you need to save each year, you can use the concept of future value of an annuity. The future value of an annuity formula is:
FV = P * ((1 + r)^n - 1) / r
Where:
FV = Future value of the annuity (target amount)
P = Amount saved each year
r = Interest rate per period (8% or 0.08 in this case)
n = Number of periods (10 years)
In this case, you know that you need to have $50,000 at the end of 10 years. So FV = $50,000. Now, rearrange the formula to solve for P:
P = FV * r / ((1 + r)^n - 1)
Substituting the given values:
P = $50,000 * 0.08 / ((1 + 0.08)^10 - 1)
Now, calculate ((1 + 0.08)^10 - 1) and substitute the value back into the equation to find P.