Sue can either borrow 10,000 dollars for 5 years with a simple interest of 7% annually or an interest which compounds annually for 6%. How much more money, rounded to the nearest dollar, would she have to pay back for the more expensive interest
interest = 5 * 10,000 * .07 = 3500
interest = 10,000 * 1.06^5 - 10,000 = 3382.26
subtract
10000((1+.07*5)-(1+.06)^5) = 117.74
To find out how much more money Sue would have to pay back for the more expensive interest, we need to calculate the total amount of money she needs to repay for each scenario.
Let's calculate the amount Sue would have to repay with simple interest first:
Principal amount (P) = $10,000
Rate of interest (R) = 7% = 0.07
Time (T) = 5 years
Formula for calculating simple interest:
Simple Interest (SI) = P * R * T
SI = 10,000 * 0.07 * 5
SI = $3,500
Now, let's calculate the total repayment amount for the compound interest scenario:
Principal amount (P) = $10,000
Rate of interest (R) = 6% = 0.06
Time (T) = 5 years
Formula for calculating compound interest:
Compound Interest (CI) = P * (1 + R)^T - P
CI = 10,000 * (1 + 0.06)^5 - 10,000
CI = 10,000 * (1.06)^5 - 10,000
CI = 10,000 * 1.33822558 - 10,000
CI = $3,382.26 (rounded to the nearest cent)
To find out how much more money Sue would have to pay back for the more expensive interest, we subtract the repayment amount with simple interest from the repayment amount with compound interest:
Difference = CI - SI
Difference = $3,382.26 - $3,500
Difference ≈ $117
Therefore, Sue would have to pay approximately $117 more for the more expensive interest.