A loan of $1000 is to be paid back, with interest, at the end of 1 year. Aft er 3 months, a partial payment of $300 is made. Use the US Rule to determine the balance due at the end of one year, considering the partial payment. Assume a simple interest rate of 9%.

total balance due at the end of 1 year is $769.75

Step-by-step explanation:

Given data

loan amount = $1000

time period = 1 year

return = $300

rate = 9%

to find out

balance due at the end of one year

solution

we know in question $300 return after 3 month so we first calculate interest of $1000 for 3 month and than we after 3 month remaining 9 month we calculate interest for $700

interest for first 3 month = (principal * rate * time) / 100 ... 1

here time is 3 month so = 3/12 will take and rate 9 % and principal $1000

put all these value in equation 1 we get interest for first 3 month

interest for first 3 month = (principal * rate * time) / 100

interest for first 3 month = (1000 * 9 * 3/12) / 100

interest for first 3 month = $22.5

now we calculate interest for remaining 9 months i. e.

interest for next 9 months = (principal * rate * time) / 100

here principal will be $700 because we pay $300 already

interest for next 9 months = (700 * 9 * 9/12) / 100

interest for next 9 months = $47.25

now we combine both interest that will be

interest for first 3 months + interest for next 9 months = interest of 1 year

interest of 1 year = $22.5 + $47.25

interest of 1 year = $69.75

so amount will be paid after 1 year will be loan amount + interest

amount will be paid after 1 year = 1000 + 69.75

amount will be paid after 1 year is $1069.75

so total balance due at the end of 1 year = amount will be paid after 1 year - amount paid already

total balance due at the end of 1 year = $1069.75 - $300

total balance due at the end of 1 year is $769.75