How much would I have to put away annually to accumulate 50,000 in 8 years given an investment of 10% compounding savings?
let the payment be x
50000=x(1 - (1.1)^-8)/.1
let me know if you don't get $9372.20
Pva= ammount[(1+i)^-1]
________ = _
I
Pva=50000[(1+0.10)8-1
____________ =
0.10
To calculate the amount you need to put away annually to accumulate $50,000 in 8 years, given a 10% compounding savings, you can use the formula for the future value of an ordinary annuity:
FV = P * [(1 + r)^(n) - 1] / r
where:
FV = future value (desired amount of $50,000)
P = annual payment (the amount you need to put away annually)
r = interest rate per compounding period (10% or 0.10 in decimal form)
n = number of compounding periods (8 years)
First, rearrange the formula to solve for P:
P = FV * (r / [(1 + r)^(n) - 1])
Plug in the values:
P = $50,000 * (0.10 / [(1 + 0.10)^(8) - 1])
P = $50,000 * (0.10 / [1.10^(8) - 1])
Now, calculate the denominator:
1.10^(8) = 1.948717
Subtract 1 from this result:
1.948717 - 1 = 0.948717
Divide the interest rate by the result:
0.10 / 0.948717 ≈ 0.105084
Multiply this by $50,000:
0.105084 * $50,000 ≈ $5254.20
So, you would need to put approximately $5254.20 away annually to accumulate $50,000 in 8 years, given a 10% compounding savings.