Question:
Find the amount to be paid if John borrowed a sum of $5200 at 6% simple interest for 7 years.
Correct Answer
$7384
Solution And Explanation
Solution
Given,
Principal (P) = $5200
Rate of Simple Interest (SI) = 6%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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) = $5200 × 6% × 7
= $5200 ×6/100 × 7
= 5200 × 6 × 7/100
= 31200 × 7/100
= 218400/100
= $2184
Thus, Simple Interest = $2184
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 = $5200 + $2184
= $7384
Thus, Amount to be paid = $7384 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 = $5200
Rate of Simple Interest (SI) or (R) = 6%
And, Time (t) = 7 years
Thus, Amount (A)
= $5200 + ($5200 × 6% × 7)
= $5200 + ($5200 ×6/100 × 7)
= $5200 + (5200 × 6 × 7/100)
= $5200 + (31200 × 7/100)
= $5200 + (218400/100)
= $5200 + $2184 = $7384
Thus, Amount (A) to be paid = $7384 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $5200, the simple interest in 1 year
= 6/100 × 5200
= 6 × 5200/100
= 31200/100 = $312
Thus, simple interest for 1 year = $312
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $312 × 7 = $2184
Thus, Simple Interest (SI) = $2184
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5200 + $2184
= $7384
Thus, Amount to be paid = $7384 Answer
Similar Questions
(1) What amount will be due after 2 years if David borrowed a sum of $3200 at a 10% simple interest?
(2) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 5% simple interest.
(3) Calculate the amount due if Sarah borrowed a sum of $3850 at 8% simple interest for 4 years.
(4) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $9834 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 6% simple interest.
(6) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 6% simple interest.
(7) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $6664 to clear the loan, then find the time period of the loan.
(8) If Ashley paid $5278 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(9) How much loan did Edward borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8360 to clear it?
(10) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $9230 to clear the loan, then find the time period of the loan.