Question:
Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 8% simple interest.
Correct Answer
$10148
Solution And Explanation
Solution
Given,
Principal (P) = $5900
Rate of Simple Interest (SI) = 8%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% per annum.
Method (1) Using Formula
Calculation of Simple Interest
Formula to Calculate Simple Interest
Simple Interest (SI) = Principal × Rate × Time
Thus, Simple Interest (SI) = $5900 × 8% × 9
= $5900 ×8/100 × 9
= 5900 × 8 × 9/100
= 47200 × 9/100
= 424800/100
= $4248
Thus, Simple Interest = $4248
Calculation of Amount
The total money paid to the lender by a borrower is called the Amount.
In other words, sum of priciple and interest is called the Amount.
Formula to Calculate the Amount
Amount = Principal + Interest
Thus, Amount = $5900 + $4248
= $10148
Thus, Amount to be paid = $10148 Answer
Method (2)
Calculation of Amount when Principal, Rate of Simple Interest and Time are given
Calculation of Amount directly using Principal, SI, and Time
Formula to calculate the Amount
Amount (A) = Principal (P) + Principal(P) × Rate of Interest (SI) × Time (t)
⇒ A = P + PRT
Here in the question, P = $5900
Rate of Simple Interest (SI) or (R) = 8%
And, Time (t) = 9 years
Thus, Amount (A)
= $5900 + ($5900 × 8% × 9)
= $5900 + ($5900 ×8/100 × 9)
= $5900 + (5900 × 8 × 9/100)
= $5900 + (47200 × 9/100)
= $5900 + (424800/100)
= $5900 + $4248 = $10148
Thus, Amount (A) to be paid = $10148 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $5900, the simple interest in 1 year
= 8/100 × 5900
= 8 × 5900/100
= 47200/100 = $472
Thus, simple interest for 1 year = $472
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $472 × 9 = $4248
Thus, Simple Interest (SI) = $4248
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5900 + $4248
= $10148
Thus, Amount to be paid = $10148 Answer
Similar Questions
(1) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6930 to clear the loan, then find the time period of the loan.
(2) If Ashley paid $5096 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(3) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $8360 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 6% simple interest.
(5) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 3% simple interest.
(6) If Kenneth paid $6000 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(7) If Karen paid $4266 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(8) Kimberly had to pay $4929 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(9) Sandra had to pay $4850.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(10) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 4% simple interest.