Question:
Find the amount to be paid if Joseph borrowed a sum of $5700 at 8% simple interest for 7 years.
Correct Answer
$8892
Solution And Explanation
Solution
Given,
Principal (P) = $5700
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) = $5700 × 8% × 7
= $5700 ×8/100 × 7
= 5700 × 8 × 7/100
= 45600 × 7/100
= 319200/100
= $3192
Thus, Simple Interest = $3192
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 = $5700 + $3192
= $8892
Thus, Amount to be paid = $8892 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 = $5700
Rate of Simple Interest (SI) or (R) = 8%
And, Time (t) = 7 years
Thus, Amount (A)
= $5700 + ($5700 × 8% × 7)
= $5700 + ($5700 ×8/100 × 7)
= $5700 + (5700 × 8 × 7/100)
= $5700 + (45600 × 7/100)
= $5700 + (319200/100)
= $5700 + $3192 = $8892
Thus, Amount (A) to be paid = $8892 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 $5700, the simple interest in 1 year
= 8/100 × 5700
= 8 × 5700/100
= 45600/100 = $456
Thus, simple interest for 1 year = $456
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $456 × 7 = $3192
Thus, Simple Interest (SI) = $3192
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5700 + $3192
= $8892
Thus, Amount to be paid = $8892 Answer
Similar Questions
(1) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $9350 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 5% simple interest.
(3) Calculate the amount due if Patricia borrowed a sum of $3150 at 4% simple interest for 3 years.
(4) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $10758 to clear the loan, then find the time period of the loan.
(5) If Ashley paid $4914 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(6) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 7% simple interest?
(7) Find the amount to be paid if John borrowed a sum of $5200 at 10% simple interest for 8 years.
(8) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 10% simple interest.
(9) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $7310 to clear the loan, then find the time period of the loan.
(10) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $10240 to clear the loan, then find the time period of the loan.