PPI wants to accumulate a fund of $100,000 in six years (by December 31, 2021) t

Question

PPI wants to accumulate a fund of $100,000 in six years (by December 31, 2021) to retire a long-term note. Four years ago, the board of directors had passed a resolution instructing the treasurer to make ten equal annual deposits in a fund earning 8% compounded annually. Because no one knew how to compute the equal deposits, the treasure decided to deposit $10,000 at the end of each year. The fourth deposit was made on December 31, 2015. What equal annual deposits should be made during the next six years, starting on Dec 31, 2016, if exactly $100,000 is to be accumulated in the fund?

Explanation / Answer

Pmt $10,000.00 Rate 8% Number of years 4 P = PMT x [((1+r)^n-1) / r] First we need to caluculate the money in account after 4 years We wil the future value of ordinary annuity Amount = 10000 x ([((1+.08)^4 - 1)/.08] $     45,061 We have 45061.12 in the account after 4 years Now we need to get = (100,000 - 45061) $     54,939 100000 = 45061 x (1+r)^n + pmt x ((1-(1/1+r)^n))/r) 100000 = 71506 + pmt x ((1-(1/1+r)^n))/r) 100000 - 71506 = pmt x ((1-(1/1+r)^n))/r) 28493 = pmt x 4.62288 Pmt = 28493 / 4.62288 $ 6,163.66

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