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Tv Installments

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Tv Installments


1. **State the problem:** You bought a TV for 800 sh and will pay it off in 18 equal monthly payments. Each month, interest of 1.5% is applied to the unpaid balance. 2. **Find the monthly payment:** This is a loan amortization problem where payments cover interest plus principal. The monthly interest rate is $i = 0.015$. Total loan $P = 800$, number of payments $n = 18$. The formula for the monthly installment amount $A$ is: $$ A = P \times \frac{i(1+i)^n}{(1+i)^n - 1} $$ Calculate: - $(1+i)^n = (1.015)^{18} \approx 1.30477$ - Numerator: $0.015 \times 1.30477 = 0.01957$ - Denominator: $1.30477 - 1 = 0.30477$ So, $$ A = 800 \times \frac{0.01957}{0.30477} = 800 \times 0.06426 = 51.41 $$ Therefore, the monthly payment is approximately 51.41 sh. 3. **Find total amount paid:** $$ 51.41 \times 18 = 925.38 $$ 4. **Calculate total interest paid:** $$ \text{Interest} = \text{Total paid} - \text{Principal} = 925.38 - 800 = 125.38 $$ **Final answers:** - Monthly payment: $51.41$ sh - Total interest paid: $125.38$ sh