Final answer:
To find out how much Oliver will have paid after 7 years for his $5,400 furniture purchase on credit at a 9.5% interest rate compounded quarterly, we use the compound interest formula. The total amount paid after 7 years will be $10,964.65.
Step-by-step explanation:
Oliver has spent $5,400 on furniture which he has purchased on credit with a 9.5% interest rate compounded quarterly. To calculate the total amount he would have paid after 7 years, we need to use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for, in years.
Using the given information:
- P = $5,400
- r = 9.5% = 0.095
- n = 4 (compounded quarterly)
- t = 7 years
We can calculate the total amount paid after 7 years as follows:
A = 5400(1 + 0.095/4)^(4*7)
A = 5400(1 + 0.02375)^(28)
A = 5400(1.02375)^(28)
A = 5400 * 2.03049
A = $10964.65
So, Oliver will have paid a total of $10,964.65 after 7 years if he buys the furniture on credit with the given interest terms.