Nathaniel want to buy a new bike. His payment options are:
Option 1: Pay $2055.99 cash. He only has $400.00 saved up, so he can take out a loan for the rest from his bank at a rate of 7.25% per annum over 2 years.
Option2: Take the store payment plan of 12 monthly payments of $180.00.
A.) If he chooses option 1, what will his monthly payment be?
B.) If he chooses Option 2, what annual rate of interest will he pay?
C) Calculate the total cost of each option. Which option should he choose, and why?
A) To calculate the monthly payment if Nathaniel chooses option 1, we need to find out how much he needs to borrow from the bank. The bike costs $2055.99, and Nathaniel already has $400 saved up. Therefore, he needs to borrow $2055.99 - $400 = $1655.99.
Next, we need to calculate the interest Nathaniel will pay on the loan. The rate of interest is 7.25%, and he will take out the loan for 2 years. To calculate the total interest, we can use the formula:
Interest = Principal * Rate * Time
Interest = $1655.99 * 0.0725 * 2 = $239.86
Now, let's calculate the total amount Nathaniel needs to repay:
Total amount = Principal + Interest = $1655.99 + $239.86 = $1895.85
Since the loan is taken out for 2 years, the monthly payment can be calculated by dividing the total amount by the number of months:
Monthly payment = Total amount / Number of months = $1895.85 / 24 ≈ $78.99
Therefore, if Nathaniel chooses option 1, his monthly payment will be approximately $78.99.
B) If Nathaniel chooses option 2, he will be paying monthly payments of $180.00 for a year. We can calculate the annual interest rate using the formula:
Total payments = Monthly payment * Number of months
Total payments = $180.00 * 12 = $2160.00
Since the total payments equal the price of the bike, there is no additional interest being charged. Therefore, the annual rate of interest is 0%.
C) Let's calculate the total cost of each option:
Option 1: Total cost = Principal + Interest = $1655.99 + $239.86 = $1895.85
Option 2: Total cost = Total payments = $180.00 * 12 = $2160.00
Comparing the total costs of both options, we can see that Option 1 has a lower total cost ($1895.85) compared to Option 2 ($2160.00). Therefore, Nathaniel should choose Option 1 because it will cost him less in the long run.