Question

Find the amount of each payment to be made into a sinking fund which earns 9​% compounded quarterly and produces ​$43 comma 000 at the end of 3.5 years. Payments are made at the end of each period.

Answer 1

$2647.18

Explanation:

Formula :
`A[(1+((r)/(n))^(n)-1 )/(((r)/(n) ))]`

Future value = $43,000

r = rate of interest = 9% = 0.09

t = 3.5 years (compounded quarterly)

n = number of compounding (3.5 × 4) = 14

Now put the values into formula :

43000 =
`A[(1+((0.09)/(4))^(14)-1 )/(((0.09)/(4) ))]`

`43000=A(((1+0.0225)^(14)-1)/((0.09)/(4)))`

`43000=A(((1.0225)^(14)-1)/(0.0225))`

43000=A(
`(0.365483427)/(0.0225))`

43,000 = A(16.243708)

A =
`(43000)/(16.243708)`

A = $2,647.17883 ≈ $2647.18