Mrs. Jessica wants to buy a flat screen television on hire purchase. The cash price is ksh.28.000.She can pay the cash price or make a down payment of ksh.8000 and 15 monthly installments of ksh .2000 each. Calculate the rate of compound interest per month. (3 marks)

Bei ya pesa taslimu ni Ksh. 28,000. Malipo ya awali ni Ksh. 8,000.
Kiasi cha mkopo ni bei ya pesa taslimu ukitoa malipo ya awali.

$$\text{Kiasi cha mkopo} = \text{Ksh. } 28,000 - \text{Ksh. } 8,000 = \text{Ksh. } 20,000$$

Kuna awamu 15 za kila mwezi, na kila awamu ni Ksh. 2,000.

$$\text{Jumla ya malipo ya awamu} = 15 \times \text{Ksh. } 2,000 = \text{Ksh. } 30,000$$

Tunatumia fomula ya riba ya kiwanja kwa malipo ya awamu, ambapo $A$ ni jumla ya kiasi kilicholipwa, $P$ ni kiasi cha mkopo, $r$ ni kiwango cha riba kwa mwezi, na $n$ ni idadi ya awamu.

$$A = P(1 + r)^n$$

Tunajua $A = \text{Ksh. } 30,000$, $P = \text{Ksh. } 20,000$, na $n = 15$. Tunahitaji kutafuta $r$.

$$30,000 = 20,000(1 + r)^{15}$$

Gawanya pande zote mbili kwa 20,000:

$$\frac{30,000}{20,000} = (1 + r)^{15}$$ $$1.5 = (1 + r)^{15}$$

Chukua mzizi wa 15 wa pande zote mbili:

$$(1.5)^{\frac{1}{15}} = 1 + r$$ $$1.02745 \approx 1 + r$$

Toa 1 kutoka pande zote mbili:

$$r \approx 1.02745 - 1$$ $$r \approx 0.02745$$

Ili kupata asilimia, zidisha kwa 100:

$$r \approx 0.02745 \times 100\%$$ $$r \approx 2.745\%$$

Kiwango cha riba ya kiwanja kwa mwezi ni takriban 2.745%.

$$\boxed{2.745\%}$$