Answer:
a) k = $1734.86 per year
b) $5244.02
Step-by-step explanation:
Principal ( borrowed ) = $6900
Annual interest rate = 18% ( compounded continuously )
Borrower makes a continuous payment at a constant rate : $k per year
a) Determine payment rate required to payoff loan ( in 7 years )
let loan at time ( t ) = x
x = $6900 , at t = 0
rate of increase of loan amount = 0.18x
rate of decrease of loan amount = k
∴ net change of loan x
= dx/dt = 0.18x - k
hence ; dt = dx / ( 0.18x - k )
k = $1734.86 per year
attached below is a part of the solution
b) Determine how much interest is paid during 7-year period
Interest paid in 7 years
= Amount paid - principal amount
= ( 1734.86 * 7 ) - 6900
= $5244.02