Loan #1
Year Amount owed
1 $3796
2 $3942
3 $4088
Loan # 2
Year Amount owed
1 $977.53
2 $1036.18
3 1098.35
For loan #1 is simple interest. Loan #2 is compound interest
How much was each loan originally
Determine the future value of each loan after 10 years
To determine the original amount for each loan, we can use the formula for simple and compound interest.
For Loan #1 (simple interest):
The formula for calculating simple interest is:
I = P * r * t
where:
I is the interest
P is the principal amount (original amount)
r is the interest rate per period
t is the number of periods
From the given information, we have:
Year 1:
Amount owed = $3796
We know that the amount owed after 1 year is the principal amount plus the interest, so:
$3796 = P + (P * r * 1)
Simplifying the equation:
$3796 = P + P * r
Similarly, we can use the given information for Year 2 and Year 3 to create the following equations:
$3942 = P + P * r
$4088 = P + P * r
Now you can solve this system of equations to find the value of P (the original amount) and r (the interest rate per period).
For Loan #2 (compound interest):
To determine the original amount for Loan #2, we need the formula for compound interest:
A = P * (1 + r/n)^(n*t)
where:
A is the final amount (amount owed after t years)
P is the principal amount (original amount)
r is the interest rate per period
n is the number of times interest is compounded per year
t is the number of years
From the given information, we have:
Year 1:
Amount owed = $977.53
We know that:
$977.53 = P * (1 + r/n)^(n*1)
Similarly, we can use the given information for Year 2 and Year 3 to create the following equations:
$1036.18 = P * (1 + r/n)^(n*2)
$1098.35 = P * (1 + r/n)^(n*3)
Now you can solve this system of equations to find the value of P (the original amount), r (the interest rate per period), and n (the number of times interest is compounded per year).
To determine the future value of each loan after 10 years, we can use the formulas for simple and compound interest:
For Loan #1 (simple interest):
Future Value = Principal + (Principal * Interest Rate * Time)
For Loan #2 (compound interest):
Future Value = Principal * (1 + Interest Rate/N)^(N*Time)
Using the values calculated earlier for the original amount (Principal), interest rate (r or Interest Rate), and compounding frequency (n or N), substitute them into these formulas to find the future value of each loan after 10 years.