Solution needed .
You need to have $50000 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 deposits 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)?
Potangnang accumulate yan
You need to have $50000 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 deposits 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
Answer
To calculate the amount you need to save each year, we can use the concept of the future value of an ordinary annuity formula. The future value of an ordinary annuity is given by the formula:
FV = P * ((1 + r)^n - 1) / r
Where:
FV is the future value of the annuity (the amount you want to accumulate)
P is the amount you save each year
r is the annual interest rate
n is the number of years
In this case, we have:
FV = $50,000
r = 8% = 0.08 (converted to decimal)
n = 10 years
We need to solve for P, which represents the amount you need to save each year. Rearranging the formula, we have:
P = FV * (r / ((1 + r)^n - 1))
Substituting the given values into the formula, we get:
P = $50,000 * (0.08 / ((1 + 0.08)^10 - 1))
Calculating this expression, we find that you need to save approximately $4,158 each year (to the nearest dollar) in order to accumulate $50,000 in 10 years.
I hope this helps! Let me know if you have any further questions.