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