Question

Mia has a student loan that is in deferment, meaning that she does not need to make payments right now. The balance of her loan account during her deferment can be represented by the function
`f(x)= 35000 (1.0325)^x` , where x is the number of years since the deferment began. If the bank decides to calculate her balance showing a monthly growth rate, an approximately equivalent function would be?

Answer 1

the approximately equivalent function with a monthly growth rate would be:

g(x) = 35000(1 + 0.002041)^12x

Explanation:

The given function f(x) = 35000(1.025)^x represents the balance of Mia's student loan during her deferment, where x is the number of years since the deferment began.

To calculate an approximately equivalent function with a monthly growth rate, we need to convert the annual growth rate (1.025) to a monthly growth rate.

To find the monthly growth rate, we need to divide the annual growth rate by the number of compounding periods in a year. Since there are 12 months in a year, the monthly growth rate is calculated as follows:

Monthly growth rate = (1 + Annual growth rate)^(1/number of compounding periods) - 1

In this case, the monthly growth rate is approximately:

Monthly growth rate = (1 + 0.025)^(1/12) - 1 ≈ 0.002041

Therefore, the approximately equivalent function with a monthly growth rate would be:

g(x) = 35000(1 + 0.002041)^12x

Note that this new function assumes that the growth rate remains constant over each month.