Question

Which of these expressions can be used to calculate the monthly payment fora 25-year loan for $305,000 at 7.8% interest, compounded monthly?O A.$305 000 0.0065(1 +0.0065) 300(1+0.0065)300 +1B.$305 000 0.0065(1 -0.0065)300(1 -0.0065 )300 +1C.$305 p00.0.0065(1 -0.0065)300(1 -0.0065)300 - 1D.$305 000 0.0065(1 +0.0065)300(1 +0.0065) 3001

Answer 1

Given:

The principal value is P = 305,000.

The annual interest rate is r = 7.8%.

The time period is t = 5 years.

Explanation:

The formula of equally monthly installment is,

$\text{EMI}=\frac{r(1+r)^n}{(1+r)^n-1}\cdot P$

Here, n is number of months, P is principal value and t is monthly rate of interest.

Determine the number of months in 25 years.

$25\cdot12=300\text{ months}$

The monthly interset rate is,

$\frac{0.078}{12}=0.0065$

Substitute the values in the formula to determine the equation for equally monthly installments.

$\begin{gathered} \text{EMI}=\frac{0.0065(1+0.0065)^{300}}{(1+0.0065)^{300}-1}\cdot305000 \\ =\frac{305000\cdot0.0065(1+0.0065)^{300}}{(1+0.0065)^{300}-1} \end{gathered}$

Option D is correct.