Question

Mia Salto wishes to determine how long it will take to repay a

Answer 1

Answer: 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

annual​end-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