Find the amount of time needed for the sinking fund to reach the given accumulated amount. (Round your answer to two decimal places.) $245 monthly at 5.7% to accumulate $25,000.
Use this formula to calculate the required period:
FV=P{[1 + R]^N - 1/ R}
25,000 = 245 x {[ 1 + 0.057/12]^N - 1 / (0.057/12]}
25,000 = 245 x {[ 1 + 0.00475]^N - 1 / (0.00475)}
25,000 = 245 x {[1.00475]^N - 1 / (.00475)} divide both sides by 245
102.040816 ={[1.00475]^N - 1 / (0.00475)}
Solve for N:
102.041 = 210.526 (1.00475^N - 1)
102.041 = 210.526 (1.00475^N - 1) is equivalent to 210.526 (1.00475^N - 1) = 102.041:
210.526 (1.00475^N - 1) = 102.041
Divide both sides by 210.526:
1.00475^N - 1 = 0.484694
Add 1 to both sides:
1.00475^N = 1.48469
Take the logarithm base 1.00475 of both sides:
Answer: | N = 83.3993 =83.40 Months, or about 6 years and 11.4 months.
Would've been helpful to also add if the interest was compounded yearly or monthly.
As a general rule, if the compounding period is not specified, then the interest rate is taken as being compounded in tandem with the periodic payments. As in this case, the interest rate is taken as being compounded monthly, in tandem with the monthly payments, hence dividing it by 12 months.
