Question:
Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 7% simple interest.
Correct Answer
$8840
Solution And Explanation
Solution
Given,
Principal (P) = $5200
Rate of Simple Interest (SI) = 7%
Time (t) = 10 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) = $5200 × 7% × 10
= $5200 ×7/100 × 10
= 5200 × 7 × 10/100
= 36400 × 10/100
= 364000/100
= $3640
Thus, Simple Interest = $3640
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 + $3640
= $8840
Thus, Amount to be paid = $8840 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) = 7%
And, Time (t) = 10 years
Thus, Amount (A)
= $5200 + ($5200 × 7% × 10)
= $5200 + ($5200 ×7/100 × 10)
= $5200 + (5200 × 7 × 10/100)
= $5200 + (36400 × 10/100)
= $5200 + (364000/100)
= $5200 + $3640 = $8840
Thus, Amount (A) to be paid = $8840 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 $5200, the simple interest in 1 year
= 7/100 × 5200
= 7 × 5200/100
= 36400/100 = $364
Thus, simple interest for 1 year = $364
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $364 × 10 = $3640
Thus, Simple Interest (SI) = $3640
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5200 + $3640
= $8840
Thus, Amount to be paid = $8840 Answer
Similar Questions
(1) Find the amount to be paid if Richard borrowed a sum of $5600 at 9% simple interest for 8 years.
(2) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $10664 to clear the loan, then find the time period of the loan.
(3) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $9632 to clear the loan, then find the time period of the loan.
(4) How much loan did Edward borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9120 to clear it?
(5) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $6956 to clear the loan, then find the time period of the loan.
(6) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 10% simple interest?
(7) Thomas had to pay $4370 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(8) Calculate the amount due if Mary borrowed a sum of $3050 at 8% simple interest for 3 years.
(9) If Betty paid $4590 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(10) In how much time a principal of $3000 will amount to $3180 at a simple interest of 2% per annum?