Respuesta :
Answer : $4938.80
A sinking fund is a term that can be broadly used to describe putting a fixed amount of money aside at regular intervals for a given time frame and investing this money at a given interest rate with an objective of saving a desired amount of money at the end of the time period.
In finance it's referred to commonly as an annuity payment.
For this question, we can use the formula for Future Value of an annuity to arrive at the answer.
[tex] FVA = P\left [ \frac{(1+r)^{n}-1}{r}\right ] [/tex]
where
FVA = future Value of an annuity
P = periodic payment
r = interest rate per period
n = number of periods
The following information is given in the question:
FV = $120,000
Interest Rate = 8% p.a
No. of years = 5 years
No. of compounding periods in a year = 4
So,
[tex] i = \frac{Annual Interest rate}{number of compounding periods in a year} [/tex]
i =0.02
[tex] n = {number of compounding periods in a year} * no. of years [/tex]
n = 20 ( 5 * 4)
Substituting these values in the FVA equation, we have
[tex] 120000 = P\left [ \frac{(1+0.2)^{20}-1}{0.02}\right ] [/tex]
[tex] 120000 = P\left [ \frac{0.485947396}{0.02}\right] [/tex]
[tex] 120000 = P * 24.2973698 [/tex]
[tex] P= \frac{120000}{24.2973698} = 4938.806175 [/tex].
