Mantago wants to borrow $20,000 to buy a used car. he examined his budget and decides that he can afford a payment of $425 a month. if his bank offers him an apr of 7.5%, how long should he borrow the money so he can afford his monthly payment?  3.5 years 4.66 years 4.5 years 4 years

4.66 years

Step-by-step explanation:

Let us assume that it will take 't' years for him to repay the money that he would borrow.

We can use monthly cashflow formula:

Here, we have been given:

Monthly cashflow C=425

Loan amount P=20000

Interest rate AMR = 7.5%. Therefore, we have

Upon substituting these values in the formula, we get:

Upon simplifying, we get:

Upon solving this equation using a calculator, we get:

Therefore, correct answer is 4.66 years. That is, second choice from the given options.

step-by-step explanation:

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like: