Question #185122

Time to repay installment loan Mia Salto wishes to determine how long it will take

to repay a loan with initial proceeds of $14,000 where annual end-of-year install-

ment payments of $2,450 are required.

a. If Mia can borrow at a 12% annual rate of interest, how long will it take for her

to repay the loan fully?

b. How long will it take if she can borrow at a 9% annual rate?

c. How long will it take if she has to pay 15% annual interest?

d. Reviewing your answers in parts a, b, and c, describe the general relationship

between the interest rate and the amount of time it will take Mia to repay the

loan fully.

Expert's answer

a)we will find it by the formula:

"n=\\frac{ln(\\frac{S}{R}\\times r+1)}{ln(1+r)}"

r=0.12

"n=\\frac{ln(\\frac{S}{R}\\times r+1)}{ln(1+r)}=\\frac{ln(\\frac{14000}{2450}\\times 0.12+1)}{ln(1+0.12)}=4.61"

b)"n=\\frac{ln(\\frac{S}{R}\\times r+1)}{ln(1+r)}=\\frac{ln(\\frac{14000}{2450}\\times 0.09+1)}{ln(1+0.09)}=4.81"

c)"n=\\frac{ln(\\frac{S}{R}\\times r+1)}{ln(1+r)}=\\frac{ln(\\frac{14000}{2450}\\times 0.15+1)}{ln(1+0.15)}=4.43"

d)the higher the interest rate, the less time it takes to pay off the loan

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