The difference between the annuity payment paid under the annual plan and that under the monthly plan is $11,496.43.
The Annuity Difference
An annuity is a series of payments made at equal intervals such as monthly, quarterly, or annually.
The annuity payment under each of the two plans in the question can be calculated using the formula for calculating the present value of an ordinary annuity as follows:
PV = P * ((1 - (1 / (1 + r))^n) / r) …………………………………. (1)
For the annual plan, the annuity payment can be calculated using equation (1) as follows:
PV = Present value = Loan from bank = Purchase price * (100% - Percentage of down payment) = $180,000 * (100% - 20%) = $144,000
PA = P = Annuity payment under annual plan = ?
r = APR = 7%, or 0.07
n = number of periods or years = 30
Substitute the values into equation (1) and solve for PA, we have:
$144,000 = PA * ((1 - (1 / (1 + 0.07))^30) / 0.07)
$144,000 = PA * 12.4090411835059
PA = $144,000 / 12.4090411835059
PA = $11,604.44
For the monthly plan, the annuity payment can be calculated using equation (1) as follows:
PV = Present value = Loan from bank = $144,000
PM = Annuity payment under monthly plan = ?
r = APR / 12 = 7% /12 = 0.07 / 12 = 0.00583333333333333
n = number of periods or months = 30 * 12 = 360
Substitute the values into equation (1) and solve for PM, we have:
$144,000 = PM * ((1 - (1 / (1 + 0.00583333333333333))^360) / 0.00583333333333333)
$144,000 = PM * 150.307567947822
PM = $144,000 / 150.307567947822
PM = $958.04
The difference between the annuity payment paid under the annual plan and that under the monthly plan can therefore be calculated as follows:
Difference = PA – PM = $11,604.44 - $958.04 = $11,496.43
Therefore, the difference between the annuity payment paid under the annual plan and that under the monthly plan is $11,496.43.
Learn more here: brainly.com/question/13405769.
