Simple Interest Installments
1. **Problem statement:**
A customer buys a coffee machine with monthly instalments of R 527 for 60 months. The machine is insured at 13.8% per annum based on the cash price of R 22,267.61. We need to calculate:
1) The total insurance amount over 60 months.
2) The monthly insurance amount.
3) The new monthly instalment including insurance.
2. **Calculate total insurance (simple interest) over 60 months:**
The formula for simple interest is:
$$I = P \times r \times t$$
where
$P = 22,267.61$ (principal or cash price)
$r = 13.8\% = 0.138$ per annum
$t = \frac{60}{12} = 5$ years (60 months converted to years)
Substitute values:
$$I = 22,267.61 \times 0.138 \times 5$$
$$I = 22,267.61 \times 0.69 = 15,360.66$$
So, total insurance over 60 months is **R 15,360.66**.
3. **Calculate monthly insurance amount:**
Monthly insurance = Total insurance $\div$ Number of months
$$ = 15,360.66 \div 60 = 256.01$$
So, monthly insurance amount is **R 256.01**.
4. **Calculate new monthly instalment including insurance:**
Original monthly instalment = R 527
New monthly instalment = Original instalment + Monthly insurance
$$= 527 + 256.01 = 783.01$$
So, the new monthly instalment including insurance is **R 783.01**.
**Final answers:**
1. R 15,360.66
2. R 256.01
3. R 783.01