find the size of each 5 payments made at the end of each year into a 6% rate sinking fund which produces 76000 at the end of 5 years
This does not help at all.
To find the size of each payment made, we can use the sinking fund formula:
Payment = Amount / ( (1 + interest rate)^n - 1 )
Where:
Payment = Size of each payment
Amount = Total amount accumulated in the sinking fund
Interest rate = Annual interest rate as a decimal
n = Number of years
In this case, the total amount accumulated in the sinking fund is $76,000, the interest rate is 6% or 0.06, and the number of years is 5.
Payment = 76000 / ( (1 + 0.06)^5 - 1 )
Let's calculate the size of each payment:
Payment = 76000 / (1.338225 - 1)
Payment = 76000 / 0.338225
Payment ≈ $224,894.68
Therefore, the size of each payment made at the end of each year into the 6% rate sinking fund would be approximately $224,894.68.
To find the size of each payment made at the end of each year into a sinking fund, we can use the formula for the future value of an annuity.
The formula for the future value of an annuity is given by:
FV = P * [(1 + r)^n - 1] / r
Where:
FV = Future Value
P = Payment amount
r = Interest rate per period
n = Number of periods
In this case, the future value (FV) is given as $76,000, the interest rate (r) is 6% per year, and the number of periods (n) is 5 years.
Using the formula, we can rearrange it to solve for the payment amount (P):
P = FV * r / [(1 + r)^n - 1]
Replacing the values, we have:
P = $76,000 * 0.06 / [(1 + 0.06)^5 - 1]
Calculating this expression, we can find the size of each payment made at the end of each year into the sinking fund.
let the payment be P
P( 1.06^5 - 1)/.06 = 76000
P(.63709296)
P = 13482.13