Mrs. Sheela purchased a sewing machine and made a down payment of Rs.1000. She agreed to pay Rs
.60 per month thereafter for one year. If the interest Raye was 7% compounded monthly, what was the cash price of the machine?
To find the cash price of the sewing machine, we need to calculate the present value of the monthly payments and the down payment. We can use the formula for the present value of an annuity to do this.
The formula for the present value of an annuity is:
PV = PMT × ((1 - (1 + r)^-n) / r),
where:
PV = Present Value,
PMT = Payment per period,
r = interest rate per period,
n = number of periods.
In this case, the payment per period (PMT) is Rs. 60, the interest rate per period (r) is 7% divided by 12 (since it is compounded monthly), and the number of periods (n) is 12.
Let's calculate the present value of the monthly payments first:
PV_payments = 60 × ((1 - (1 + (7%/12))^-12) / (7%/12)).
Now, let's calculate the present value of the down payment:
PV_down_payment = 1000.
To find the cash price of the machine, we need to add the present value of the monthly payments and the present value of the down payment:
Cash price = PV_payments + PV_down_payment.
Let's substitute the values into the equations and calculate the cash price of the machine:
PV_payments = 60 × ((1 - (1 + (7%/12))^-12) / (7%/12)) = Rs. 700.838.
Cash price = 700.838 + 1000 = Rs. 1700.838.
Therefore, the cash price of the sewing machine is Rs. 1700.838.