Answer:
It will take about 20 years
Step-by-step explanation:
Sinking Fund involves saving an series of equal amount periodically invested at certain rate of interest to accumulate a target amount in the future. The target amount might be to finance a particular project - a vacation in this case.
Where an equal deposit is invested the sum accumulated (deposit plus interest earned) at the end of the final period is known as the Future Value (FV) of the sinking fund. The future value in this scenario = $44,000
The FV is determined as follows:
FV = Equal monthly deposit × Monthly Annuity factor
where FV- future value, A- equal cash deposit, r-rate of return, n- number of years.
A= 560, r = 10.3, n= ?
Monthly Annuity factor = 44,000/560 = 78.571
Monthly interest rate = 10.3/12=0.8583
Annuity monthly annuity factor =( (1+r)^n - 1 )/r
(1.008583^12n -1)/0.08583= 78.571
cross multiply
78.571×0.08583= 1.008583^12n -1
6.7437= 1.008583^12n -1
6.7437 + 1 = 1.008583^12n
7.7437= 1.008583^12n
find log of both sides
12n = log 7.7437/log 1.008583
12n = 239.50
n= 239.50/12 = 19.9 years.
Approximately 20 years
It will take about 20 years