Question

Marang borrowed money that must be repaid in nine payments. The first four payments of R2 000 each are paid at the beginning of each year. Thereafter five payments of R5 000 each are paid at the end of each year. Note there is only one payment per year. If money is worth 6,85% per year, then the present value of these payments is

Answer 1

PV of first 4 payments 

$=P+P\frac{(1-(1+r)^{-(n-1)}}{r}$

Where P= periodic payment=R 2000

r=rate per period=6.85%=0.0685

n=number of periods=4

Calculation of PV of first 4 payments

PV of first 4 payments $=2000+2000\frac{(1-(1+0.0685)^{-(4-1)}}{0.0685}\\=2000+2000\frac{1-0.819740553}{0.0685}\\=2000+2000\frac{0.180259447}{0.0685}\\=2000+(2000×2.63152477)\\=2000+5263.05\\=R \space 7263.05$

Calculation of PV of next 5 payments

PV of next 5 payments $=[5000÷(1+0.0685)^5] +[5000÷(1+0.0685)^6] +[5000÷(1+0.0685)^7] +[5000÷(1+0.0685)^8] +[5000÷(1+0.0685)^9]\\=3590.02+3359.87+3144.48+2942.89+2754.22\\= R 15791.48$

Total present value of 9 payments$=7263.05+15791.48\\=R23054.53$