Question

Mary owes June $750, and wants to pay her off. She decides to borrow the amount from her bank at a discount rate of 16%. If she borrows the money for 10 months, find the amount of the loan she should ask for so that her proceeds are $750?

Answer 1

To have proceeds of $750 after 10 months, Mary should ask for a loan amount of approximately $865.15 at a discount rate of 16%.

Step-by-step explanation:

To find the amount of the loan Mary should ask for, we can use the formula for discounting:

A = P(1 - rt)

Where:

A is the amount borrowed (to be determined)

P is the proceeds ($750)

r is the discount rate (16% or 0.16)

t is the time in years (10 months/12 months per year)

Plugging in the values:

A = $750 / (1 - 0.16 * (10/12))

Simplifying:

A = $750 / (1 - 0.1333)

A = $750 / 0.8667

A ≈ $865.15

Therefore, Mary should ask for a loan amount of approximately $865.15 to have proceeds of $750 after 10 months.

Answer 2

$662.77

Step-by-step explanation:

Data provided in the question:

Amount Mary owes = $750

Discount rate, r = 16%

Time period = 10 months =
`(10)/(12)` years = 0.833 years

Now,

Amount Mary owes = Loan Amount × ( 1 + r )ⁿ

or

750 = Loan amount ×
`(1+0.16)^(0.833)`

or

750 = Loan Amount × 1.131

or

Loan Amount = $662.77

The amount of the loan she should ask for so that her proceeds are $750 is $662.77