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.

Step-by-step explanation:

The formula of equally monthly installment is,

`\text{EMI}=(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,

`(0.078)/(12)=0.0065`

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

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

Option D is correct.