Question

Cooper & Cooper Development Company plans to raise $700,000 over a 2-year period so they can purchase a piece of real estate. In order to obtain this amount, the company has decided to make quarterly investments into a sinking fund that will earn 8% per year compounded quarterly for the next 2years. Using the sinking fund table calculate the amount of each quarterly sinking fund payment required to raise $700,000 in 2 years.

Sinking fund table
Period	2%	3%	4%	5%	6%	7%	8%
1	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000
2	0.4951	0.4926	0.4902	0.4878	0.4854	0.4808	0.4762
3	0.3268	0.3235	0.3203	0.3172	0.3141	0.3080	0.3021
4	0.2426	0.2390	0.2355	0.2320	0.2286	0.2219	0.2155
5	0.1922	0.1884	0.1846	0.1810	0.1774	0.1705	0.1638
6	0.1585	0.1546	0.1508	0.1470	0.1434	0.1363	0.1296
7	0.1345	0.1305	0.1266	0.1228	0.1191	0.1121	0.1054
8	0.1165	0.1125	0.1085	0.1047	0.1010	0.0940	0.0874
9	0.1025	0.0984	0.0945	0.0907	0.0870	0.0801	0.0736
10	0.0913	0.0872	0.0833	0.0795	0.0759	0.0690	0.0627

Answer 1

The annual interest rate in decimal form is 8 / 100 = 0.08, i = (0.08 / 4) = 0.02, n = (2 * 4(quarters)) = 8,

PMT = FV * i / ((1 + i)ⁿ - 1)

i / ((1 + i)ⁿ - 1) , it is already calculated in the table. We need to find the correct value which needs to be put in the formula.

As we know from above that n=8 so we will take the period as 8 and so the value will from Period 8.

As i=0.02 from above, so if we want to calculate it as a percentage then, 0.02*100%

=2%

So we will take the value from the column which has 2% interest

Taking the value from period=8 and interest=2%,

we get,

i / ((1 + i)ⁿ - 1)=0.1165

FV=$700,000

Putting it in the formula:

PMT = FV * i / ((1 + i)ⁿ - 1)

=$700,000*0.1165

=$81,550

Therefore,  amount of each quarterly sinking fund payment required to raise $700,000 in 2 years is $81,550.