Question:
Find the amount to be paid if Richard borrowed a sum of $5600 at 7% simple interest for 7 years.
Correct Answer
$8344
Solution And Explanation
Solution
Given,
Principal (P) = $5600
Rate of Simple Interest (SI) = 7%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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) = $5600 × 7% × 7
= $5600 ×7/100 × 7
= 5600 × 7 × 7/100
= 39200 × 7/100
= 274400/100
= $2744
Thus, Simple Interest = $2744
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 = $5600 + $2744
= $8344
Thus, Amount to be paid = $8344 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 = $5600
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 7 years
Thus, Amount (A)
= $5600 + ($5600 × 7% × 7)
= $5600 + ($5600 ×7/100 × 7)
= $5600 + (5600 × 7 × 7/100)
= $5600 + (39200 × 7/100)
= $5600 + (274400/100)
= $5600 + $2744 = $8344
Thus, Amount (A) to be paid = $8344 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $5600, the simple interest in 1 year
= 7/100 × 5600
= 7 × 5600/100
= 39200/100 = $392
Thus, simple interest for 1 year = $392
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $392 × 7 = $2744
Thus, Simple Interest (SI) = $2744
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5600 + $2744
= $8344
Thus, Amount to be paid = $8344 Answer
Similar Questions
(1) What amount does John have to pay after 6 years if he takes a loan of $3200 at 8% simple interest?
(2) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $10070 to clear the loan, then find the time period of the loan.
(3) How much loan did Mark borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7360 to clear it?
(4) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 7% simple interest?
(5) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 5% simple interest.
(6) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $9372 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Sarah borrowed a sum of $3850 at 8% simple interest for 3 years.
(8) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $7990 to clear the loan, then find the time period of the loan.
(9) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 3% simple interest?
(10) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 10% simple interest.