Question:
Calculate the amount due if John borrowed a sum of $3200 at 7% simple interest for 3 years.
Correct Answer
$3872
Solution And Explanation
Solution
Given,
Principal (P) = $3200
Rate of Simple Interest (SI) = 7%
Time (t) = 3 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) = $3200 × 7% × 3
= $3200 ×7/100 × 3
= 3200 × 7 × 3/100
= 22400 × 3/100
= 67200/100
= $672
Thus, Simple Interest = $672
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 = $3200 + $672
= $3872
Thus, Amount to be paid = $3872 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 = $3200
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 3 years
Thus, Amount (A)
= $3200 + ($3200 × 7% × 3)
= $3200 + ($3200 ×7/100 × 3)
= $3200 + (3200 × 7 × 3/100)
= $3200 + (22400 × 3/100)
= $3200 + (67200/100)
= $3200 + $672 = $3872
Thus, Amount (A) to be paid = $3872 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 $3200, the simple interest in 1 year
= 7/100 × 3200
= 7 × 3200/100
= 22400/100 = $224
Thus, simple interest for 1 year = $224
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $224 × 3 = $672
Thus, Simple Interest (SI) = $672
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3200 + $672
= $3872
Thus, Amount to be paid = $3872 Answer
Similar Questions
(1) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $6216 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 5% simple interest.
(3) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 10% simple interest.
(4) How much loan did Elizabeth borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6812.5 to clear it?
(5) Find the amount to be paid if Joseph borrowed a sum of $5700 at 10% simple interest for 7 years.
(6) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $8662 to clear the loan, then find the time period of the loan.
(7) What amount does James have to pay after 6 years if he takes a loan of $3000 at 5% simple interest?
(8) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $9514 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Richard borrowed a sum of $5600 at 8% simple interest for 7 years.
(10) If Susan paid $4088 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.