The periodic payment should be $1,079.59 to get the required amount.
Sinking funds accumulate money by making regular payments, and interest will keep adding up until the fund matures. As a result, it is an annuity idea.
Required amount (A) = $40,000
Time (n) = 7 years
Interest rate (i) = 8% or 0.08 (Assume it annually)
No. of payments in a year = 4 (Quarterly)
The required amount is given
Hence, the formula of FV of the annuity will apply
Let R be the payment required at the end
Computation of R:-
A = R*{(1+i/4)^n*4-1/(i/4)}
40000 = R*{(1+0.08/4)^7*4-1/(0.08/4)}
40000 = R*{(1+0.02)^28-1/(0.02)
40000 = R*{(1.02)^28-1/(0.02)
40000 = R*37.051
R = $1079.59
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