Question

A TV set is offered for sale for P1, 800 down payment, and P950 every month for thebalance for 2 years. If interest is to be computed at 6% compounded monthly, what isthe cash price equivalent of the TV set?

Answer 1

Answer:

The cash equivalent price of the tv set is P5849.37

Explanation:

The total amount paid monthly is:

The initial down payment of P1800 and 24 payments of P950 (2 years = 24 months)

Then, the price paid with interest is:

$1800+24\cdot950=24600$

Now, the formula for the monthly compound interest is:

$A=P(1+\frac{r}{12})^{12t}$

Where:

A is the amount after t years

P is the initial amount (what we want to find)

R is the rate of compound in decimal

t is the number of years of compounding

In this case:

• A = 24600 (the total paid if compounded)

,

• P is what we want to find

,

• r = 0.06 ( to convert percentage to decimal, we divide by 100: 6%/100 = 0.06)

,

• t = 24 (2 years)

$\begin{gathered} 24600=P(1+\frac{0.06}{12})^{12\cdot24} \\ . \\ 24600=P\cdot1.005^{288} \\ . \\ P=\frac{24600}{4.2056} \\ . \\ P=5849.373 \end{gathered}$

To the nearest cent, the cash price is 5849.37