Mia salto wishes to determine how long it will take to repay a
$18,000 loan given that the lender requires her to make annualend-of-year installment payments of
$4,309
.
a.  if the interest rate on the loan is
15%,
how long will it take for her to repay the loan fully?
b.  how long will it take if the interest rate is
12%?
c.  how long will it take if she has to pay
19%
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.

a. 10.2 years

b. 12.6 years

c. 8.2 years

d. n = ln 4.1773/ln (1+r)

Step-by-step explanation:

$18,000 loan

annualend-of-year installment payments of  $4,309

F = P(1+r)ⁿ

a. r = 15% = 0.15

18000 = 4309(1+0.15)ⁿ

18000/4309 = 1.15ⁿ

4.1773 = 1.15ⁿ

ln 4.1773 = ln 1.15ⁿ

ln 4.1773 = n*ln 1.15

n = ln 4.1773/ln 1.15

n = 10.2 years

b. r = 12% = 0.12

18000 = 4309(1+0.12)ⁿ

18000/4309 = 1.12ⁿ

4.1773 = 1.12ⁿ

ln 4.1773 = ln 1.12ⁿ

ln 4.1773 = n*ln 1.12

n = ln 4.1773/ln 1.12

n = 12.6 years

c. r = 19% = 0.19

18000 = 4309(1+0.19)ⁿ

18000/4309 = 1.19ⁿ

4.1773 = 1.19ⁿ

ln 4.1773 = ln 1.19ⁿ

ln 4.1773 = n*ln 1.19

n = ln 4.1773/ln 1.19

n = 8.2 years

d. The general relationship is  n = ln 4.1773/ln (1+r) r as a decimal