Question:
Find the amount to be paid if Richard borrowed a sum of $5600 at 7% simple interest for 8 years.
Correct Answer
$8736
Solution And Explanation
Solution
Given,
Principal (P) = $5600
Rate of Simple Interest (SI) = 7%
Time (t) = 8 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% × 8
= $5600 ×7/100 × 8
= 5600 × 7 × 8/100
= 39200 × 8/100
= 313600/100
= $3136
Thus, Simple Interest = $3136
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 + $3136
= $8736
Thus, Amount to be paid = $8736 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) = 8 years
Thus, Amount (A)
= $5600 + ($5600 × 7% × 8)
= $5600 + ($5600 ×7/100 × 8)
= $5600 + (5600 × 7 × 8/100)
= $5600 + (39200 × 8/100)
= $5600 + (313600/100)
= $5600 + $3136 = $8736
Thus, Amount (A) to be paid = $8736 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 8 years
= Simple interest for 1 year × 8
= $392 × 8 = $3136
Thus, Simple Interest (SI) = $3136
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5600 + $3136
= $8736
Thus, Amount to be paid = $8736 Answer
Similar Questions
(1) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $8320 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 10% simple interest.
(3) Calculate the amount due if John borrowed a sum of $3200 at 6% simple interest for 4 years.
(4) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 8% simple interest?
(5) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 3% simple interest?
(6) Calculate the amount due if Karen borrowed a sum of $3950 at 7% simple interest for 4 years.
(7) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 2% simple interest for 8 years.
(8) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $9288 to clear the loan, then find the time period of the loan.
(9) What amount will be due after 2 years if James borrowed a sum of $3000 at a 5% simple interest?
(10) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 9% simple interest for 3 years.