Jenny purchases a piano for rm 7000. She pays down payment of rm 2000 and agrees to pay the balance in 15 equal monthly payments, the first due in one month. If the dealer charges her 5% compounded monthly , find her monthly payment.
P = Po(1+r)^n.
Po = 7000 - 2000 = $5000.
r = 0.05/12mo. = 0.00417/mo.
n = 1Comp./mo. * 15mo. = 15 Compounding periods.
P/15 = Monthly payment.
To find Jenny's monthly payment, we can use the formula for the present value of an annuity:
PV = PMT × ((1 - (1 + r)^-n) / r)
Where:
PV = Present value (the initial amount borrowed or purchased)
PMT = Monthly payment
r = Monthly interest rate
n = Number of monthly payments
In this case, the present value (PV) is the balance Jenny has to pay after the down payment, which is RM 7,000 - RM 2,000 = RM 5,000.
The monthly interest rate (r) is calculated by taking the annual interest rate (5%) and dividing it by 12 (since there are 12 months in a year). Therefore, r = 0.05/12 = 0.0041667.
The number of monthly payments (n) is given as 15.
Now we can substitute these values into the formula to find the monthly payment (PMT):
RM 5,000 = PMT × ((1 - (1 + 0.0041667)^-15) / 0.0041667)
To solve for PMT, we need to isolate it on one side of the equation:
PMT = RM 5,000 / ((1 - (1 + 0.0041667)^-15) / 0.0041667)