Question:
Find the amount to be paid if Charles borrowed a sum of $5900 at 8% simple interest for 7 years.
Correct Answer
$9204
Solution And Explanation
Solution
Given,
Principal (P) = $5900
Rate of Simple Interest (SI) = 8%
Time (t) = 7 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% × 7
= $5900 ×8/100 × 7
= 5900 × 8 × 7/100
= 47200 × 7/100
= 330400/100
= $3304
Thus, Simple Interest = $3304
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 + $3304
= $9204
Thus, Amount to be paid = $9204 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) = 7 years
Thus, Amount (A)
= $5900 + ($5900 × 8% × 7)
= $5900 + ($5900 ×8/100 × 7)
= $5900 + (5900 × 8 × 7/100)
= $5900 + (47200 × 7/100)
= $5900 + (330400/100)
= $5900 + $3304 = $9204
Thus, Amount (A) to be paid = $9204 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 7 years
= Simple interest for 1 year × 7
= $472 × 7 = $3304
Thus, Simple Interest (SI) = $3304
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5900 + $3304
= $9204
Thus, Amount to be paid = $9204 Answer
Similar Questions
(1) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $11600 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Thomas borrowed a sum of $5800 at 4% simple interest for 7 years.
(3) If Elizabeth paid $4140 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(4) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $12060 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Michael borrowed a sum of $5300 at 3% simple interest for 7 years.
(6) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $7009 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if Richard borrowed a sum of $5600 at 3% simple interest for 8 years.
(8) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $9943 to clear the loan, then find the time period of the loan.
(9) In how much time a principal of $3150 will amount to $3402 at a simple interest of 4% per annum?
(10) In how much time a principal of $3150 will amount to $3622.5 at a simple interest of 3% per annum?