Question

Find the size of each of 6 payments made at the end of each year into a 6% rate sinking fund which produces $82000 at the end of 6 years. The payment size is $? rounded to the nearest cent

Answer 1

Answer:

at the end of 1st year we pay $ 11756

at the end of 2nd year we pay $ 24217

at the end of 3rd year we pay $ 37426

at the end of 4th year we pay $ 51427

at the end of 5th year we pay $ 66269

at the end of 6th year we pay $ 82001

Step-by-step explanation:

Given data

rate ( i ) = 6%

Future payment  = $82000

no of time period ( n ) = 6

to find out

size of all of 6 payments

solution

we know future payment formula i.e.

future payment = payment per period ( $(1 + rate)^{n}$ - 1 )   / rate

put all these value and get payment per period

payment per period = future payment × rate  /  ( $(1 + rate)^{n}$ - 1 )   / rate

payment per period = 82000 × 0.06  /  ( $(1 + 0.06)^{6}$ - 1 )   / rate

payment per period = 82000 × 0.06 / 0.4185

payment per period = $ 11756.27

at the end of 1st year we pay $ 11756

and at the end of 2nd year we pay $ 11756 × ( 1  + 0.06) + 11756

and at the end of 2nd year we pay $ 24217

and at the end of 3rd year we pay $ 24217 × ( 1  + 0.06) + 11756

and at the end of 3rd year we pay $ 37426

and at the end of 4th year we pay $ 37426 × ( 1  + 0.06) + 11756

and at the end of 4th year we pay $ 51427

and at the end of 5th year we pay $ 51427 × ( 1  + 0.06) + 11756

and at the end of 5th year we pay $ 66269

and at the end of 6th year we pay $ 66269 × ( 1  + 0.06) + 11756

and at the end of 6th year we pay $ 82001