An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (1)
Calculate the monthly interest rate: m o n t h l y _ in t eres t _ r a t e = 12 0.24 = 0.02 .
Calculate the total number of payments: n u mb er _ o f _ p a y m e n t s = 2 × 12 = 24 .
Apply the amortization formula to find the monthly payment: M = 4198 × ( 1 + 0.02 ) 24 − 1 0.02 ( 1 + 0.02 ) 24 ≈ 221.95 .
The amount of each payment is approximately 221.95 .
Explanation
Understanding the Problem We are given a loan of $4198 with an annual interest rate of 24%, and we need to find the monthly payment required to amortize the loan over 2 years. The payments are made monthly.
Calculating Monthly Interest Rate First, we need to convert the annual interest rate to a monthly interest rate. To do this, we divide the annual interest rate by 12: m o n t h l y _ in t eres t _ r a t e = 12 ann u a l _ in t eres t _ r a t e = 12 0.24 = 0.02
Calculating Total Number of Payments Next, we need to calculate the total number of payments. Since the loan is amortized over 2 years and payments are made monthly, we multiply the number of years by 12: n u mb er _ o f _ p a y m e n t s = n u mb er _ o f _ ye a rs × 12 = 2 × 12 = 24
Calculating Monthly Payment Now, we can use the amortization formula to calculate the monthly payment: M = P ( 1 + i ) n − 1 i ( 1 + i ) n where:
M is the monthly payment
P is the principal loan amount ($4198)
i is the monthly interest rate (0.02)
n is the number of payments (24) Plugging in the values, we get: M = 4198 × ( 1 + 0.02 ) 24 − 1 0.02 ( 1 + 0.02 ) 24 M = 4198 × ( 1.02 ) 24 − 1 0.02 ( 1.02 ) 24 M = 4198 × ( 1.608437 − 1 ) 0.02 × 1.608437 M = 4198 × 0.608437 0.03216874 M = 4198 × 0.0528718 M = 221.95
Final Answer Therefore, the amount of each payment is approximately $221.95.
Examples
Understanding loan amortization is crucial in personal finance. For instance, when buying a car or a house, the amortization schedule helps you see how much of each payment goes towards the principal versus the interest. This knowledge allows you to make informed decisions about prepaying loans or refinancing to save money on interest over the life of the loan. It also helps in budgeting and planning your finances effectively.
