Problema Solution
A company wishes to have 15 million as their fund at the end of 10 years. How much will they deposit at the end of each year, if it earns 12% compounded quarterly?
Answer provided by our tutors
Sinking fund formula is:
S = R[((1 + i)^n - 1)/i]
where
S = $15,000,000 is the future value;
R is the periodic payment each quarter;
i = 0.12/4 = 0.03 is the interest rate per period (since it is compounded quarterly);
n = 4*10 = 40 is the number of periods (since it is compounded quarterly);
R = S/[((1 + i)^n - 1)/i]
R = Si/((1 + i)^n - 1)
R = (15000000*0.03)/((1 + 0.03)^40 - 1)
R = $198,935.67
They should deposit $198,935.67 each quarter.