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
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#1 - simple interest,
interest earned in 1st year = 3942-3796 = 146
rate = 146/3796 = .0385 or 3.85%
check : is 2(146) + 3796 = 4088 ? , YES!
#2, let the rate be i
for 1st year ...
977.53(1+i) = 1036.18
1+i = 1.059998
i = .059998 or .06 = 6%
check: is 977.53(1.059998)^2 = 1098.35 ? YES!
To determine the original amount of each loan, you need to find the principal or initial amount when the loan started. In the case of Loan #1, it is not explicitly provided. However, you can calculate the principal amount by subtracting the interest from the total amount owed.
For Loan #1:
Year 1: Amount owed = Principal + Interest = $3796
Year 2: Amount owed = Principal + Interest = $3942
Year 3: Amount owed = Principal + Interest = $4088
From the given information, it seems like the interest is the same for each year, but we need to calculate the exact interest rate. To do this, we can subtract the amount owed at Year 1 from the amount owed at Year 2, and divide it by the principal amount:
Interest = (Amount owed at Year 2 - Amount owed at Year 1) / Principal
Interest = ($3942 - $3796) / Principal
Similarly, we can find the interest for Year 3:
Interest = (Amount owed at Year 3 - Amount owed at Year 2) / Principal
Interest = ($4088 - $3942) / Principal
Since Loan #1 is simple interest, we assume that the interest remains constant throughout the years. Hence, we can take the average of these two interest values and calculate the principal amount:
Average Interest = (Interest Year 1 + Interest Year 2) / 2
Now, let's move on to Loan #2 which is compound interest. In this case, the given information provides the amount owed at each year, but not the interest rate. We can use the compound interest formula to calculate the principal amount and the future value after 10 years.
To calculate the future value with compound interest, we use the formula:
Future Value = Principal * (1 + Interest Rate)^Number of Years
Let's calculate the future value after 10 years for each loan.