Problema Solution
A condominium association decided to set up a sinking fund to accumulate $50,000 by the end of 4 years to build a new sauna and swimming pool. What quarterly deposits are required if the annual interest rate is 4.6% and it is compounded quarterly?
Answer provided by our tutors
S = $50,000 is the future value
r = 4.6% = 0.046 yearly interest rate
i = r/12 = 0.046/4 interest rate per quarter
n = 4*4 = 16 number of payment periods
R = the quarter payment quarterly deposits)
S = R[((1 + i)^n - 1)/i]
R = Si/((1 + i)^n - 1)
R = (50000*0.046/4)/(((1 + 0.046/4)^(16)) - 1)
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R = $2,864.20 rounded to the nearest cent
$2,864.20 quarterly deposits are require.