Question

Solly will discharge a debt of R500 000 six years from now, using the sinking fund method. The debt’s interest

is 15,6% per year, paid quarterly. The sinking fund will earn interest at a rate of 8,4% per year, compounded

monthly.

The monthly deposit into the sinking fund will equal

[1] R4 236,10.

[2] R5,364,60.

[3] R10 736,10.

[4] R12 958,53.

[5] R16 235,96.

 

The total yearly cost to discharge the debt (to the nearest rand) will equal

[1] R42 000.

[2] R78 000.

[3] R93 834.

[4] R128 833.

[5] R142 375.

Answer 1

Let s be the monthly deposit into the sinking fund. The first deposit will grow to s(1+8.4/1200)=1.007s after a month when the next deposit is added. There will be 6*12=72 deposits over 6 years which must pay off the R500,000, while its interest is paid off quarterly.

The sinking fund's first deposit gains the most since it has 71 months to accumulate; the second deposit has 70 months; the third 69 months; and so on, so we have a series: s(1.007^71+...+1). The series in the parentheses we'll call S and its sum as a geometrical progression is (1.007^72-1)/0.007=93.2036, making the total amount accrued after 6 years 93.2036s.

So this amount pays off the debt and 93.2036s=500000, s=R5364.60 (answer [2]).

If, in addition, the debt's interest has to be paid quarterly (15.6/4%=15.6/400=0.039) then this interest amounts to 500000*0.039=R19,500 per quarter. This means that Solly pays 4*19500=R78000 a year in interest on the debt. Added to this is 12 months' worth monthly deposit into the sinking fund=78000+12*5364.60=R142,375.20, or R142,375 to the nearest rand, Solly's yearly cost (answer [5]).