Answer:
The principal of the loan is $350000
$26844 is not half 54886 so the statement is not true
Step-by-step explanation:
* Lets use the given rule to solve the question
- The total loan amount to be paid = p (1 + r)^t , where
# t is time in years,
# r is interest rate as a decimal
# p is the principal of the loan
- To find t divide the number of months by 12
∵ t = 30/12 = 2.5 years
∵ r = 6/100 = 0.06 ⇒ the interest rate in decimal
∵ The total loan amount to be paid = $404,886
∴ 404,886 = p (1 + 0.06)^2.5
∴ 404,886 = p (1.06)^2.5 ⇒ divide both sides by (1.06)^2.5
∴ p = 404,886 ÷ [(1.06)^2.5] ≅ $350,000
* The principal of the loan is $350,000
- To check the statement of the manager lets find the difference
between the total loan amount and the principal
∵ The principal of the loan is $350,000
∵ the total loan amount to be paid is $404,886
∴ The difference = 404,886 - 350,000 = $54886
- Lets find the total loan amount to be paid when the interest rate
was cut in half
∵ The total loan amount to be paid = p (1 + r)^t
∵ t = 30/12 = 2.5 years
∵ The half of 6% is 3%
∴ r = 3/100 = 0.03 ⇒ the interest rate in decimal
∵ p = $350,000
∴ The total loan amount to be paid = 350,000 (1 + 0.03)^2.5
∴ The total loan amount to be paid = 350,000 (1.03)^2.5
∴ The total loan amount to be paid = $376,844
- Lets find the difference between the total amount to be paid and
the principal
∴ The difference = 376,844 - 350,000 = $26844
∵ $26844 is not half 54886
* The statement is not true
