SOLUTION: Maria wants to buy a car but has little money. The dealer offers $5,000 at 12% compounded daily for 7 years. Maria doesn't have to make monthly payments, but must pay off the loan

Question 756248: Maria wants to buy a car but has little money. The dealer offers $5,000 at 12% compounded daily for 7 years. Maria doesn't have to make monthly payments, but must pay off the loan in full after 7 years. How much must Maria pay?

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
assuming there are 365 days in a year, the daily interest rate is equal to .12 divided by 365 which is equal to .000328767 per day.

the number of time periods is equal to 365 * 7 which is equal to 2555.

add 1 to the interest rate per day and raise that to the power of 2555 to get:

1.000328767 ^ 2555 = 2.316047218

multiply 5000 by 2.31..... to get 11580.23609

at the end of 7 years, she will have to pay the dealer $11,580.24.

with no payments, this is a future value of a present amount formula which is:

f = p * (1 + i/c) ^ (y * c)

f = future value
p = present amount
i = annual interest rate (apr)
c = number of compounding periods per year.
y = number of years

based on your information and assuming 365 days per year, the formula becomes:

f = 5000 * (1 + (.12/365)) ^ (7*365)

that becomes:

f = 5000 * 1.000328767 ^ 2555

use your calculator to get:

f = 11580.23609

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