Question

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:

Data provided in the question:

Rate = 9% compounded quarterly

interest rate per period, i = 9% ÷ 4 = 2.25% = 0.0225

Future value = $43,000

Time = 3.5 years

Number of periods, = 3.5 × 4 = 14

Now,

Let the annual payments be 'A'

Thus,

Future value = A × [ (1 + i)ⁿ - 1 ) ÷ i ]

or

$43,000 = A × [ (1 + 0.0225)¹⁴ - 1 ) ÷ 0.0225 ]

or

$43,000 = A × 16.244

or

A = $2647.18