Answer to Question #197952 in Financial Math for Beauty Magadlela

Question

Frieda will discharge a debt of R500 000 six years from now, using the sinking fund method. The interest of the debt is 15,6% per year, paid quarterly. The sinking fund earns interest at a rate of 8,4% per year, compounded monthly.

The monthly deposit into the sinking fund is

[1] R12 958,53.

[2] R10 736,10.

[3] R5,364,60.

[4] R4 236,10.

[5] R16 235,96

Answer 1

Correct answer is [5] R162,35,96

First of all, we will have to find the payment made into the sinking fund

for that we will use the following formula

$PMT = FV [ \frac{i }{( (1+i)^n - 1)} ]$

Where

PMT = periodic payment into the fund

FV = future value (value of debt in our case)

i = monthly interest rate

n = number of months

Please note that we will take monthly interest rate $(\frac{8.4\% }{12 }= 0.7\%)$ and number of periods in months $(6 \times12 = 84)$ as interest rate is compounding monthly for the sinking fund. 

Using the formula from step 1

$PMT = 500,000 [ \frac{0.007 }{ ( (1+0.007)^{84} - 1) }]$

$= 500,000 [\frac{ 0.007 }{ ( 1.65243 - 1)} ]$

$= 500,000 (\frac{ 0.007 }{0.65243} )$

$= 500,000 \times 0.010729195$

$= 5,364.6$

Since this is monthly payment into the sinking fund, we will multiply it by 12 to find the annual payment into the sinking fund 

$= 5,364.6 \times12 = 64,375.17$

Thus, Annual payments into the sinking fund is R64,375.17.

Now we will find the annual cost of debt, to find that, we will simply multiply the total debt amount by the annual interest rate.

$= 500,000 \times 0.156 = R78,000$

Annual cost of debt = R78,000 

Now to find the yearly cost to retire the debt, we will simply add the annual amount paid into sinking fund and annual cost of debt

yearly cost to retire the debt = R78,000 + 64,375.17

yearly cost to retire the debt = R162,35,96