Homework Answers
Annual level sinking fund deposit amount is $ 5,216.23
Balance in sinking fund at time 5 is $ 28,708.03
Total payment in the 6th payment is $ 9,961.23
Principal in the 6th payment is $ 5,216.23 (i.e. payment for sinking fund)
Explanation:
Annual payment of sinking fund can be computed using formula for FV of annuity as:
FV = C x [(1+r) n -1/r]
C = FV / [(1+r) n -1/r]
FV = Future value of annuity = $ 65,000
C = Annual cash deposit
r = Rate of interest = 0.048
n = Number of periods = 10
Substituting the values on above formula, we get C as:
C = $ 65,000 / [(1+0.048) 10 -1/0.048]
= $ 65,000 / [(1.048) 10 -1/0.048]
= $ 65,000 / [(1.59813265811379-1)/0.048]
= $ 65,000 / (0.59813265811379 /0.048)
= $ 65,000 / 12.4610970440374
= $ 5,216.23415420735 or $ 5,216.23
Balance in sinking fund at time 5 can be computed using same above formula for FV of annuity as:
FV = C x [(1+r) n -1/r]
= $ 5,216.23 x [(1+0.048) 5 -1/0.048]
= $ 5,216.23 x [(1.048) 5 -1/0.048]
= $ 5,216.23 x [(1.26417271688397 -1)/0.048]
= $ 5,216.23 x (0.26417271688397/0.048)
= $ 5,216.23 x 5.503598268416
= $ 28,708.0343956596 or $ 28,708.03
Annual interest payment = Principal x rate = $ 65,000 x 0.073 = $ 4,745
Total payment in the 6th payment = $ 4,745 + $ 5,216.23 = $ 9,961.23
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