Question:
Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 10% simple interest.
Correct Answer
$10400
Solution And Explanation
Solution
Given,
Principal (P) = $5200
Rate of Simple Interest (SI) = 10%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 10
= $5200 ×10/100 × 10
= 5200 × 10 × 10/100
= 52000 × 10/100
= 520000/100
= $5200
Thus, Simple Interest = $5200
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 + $5200
= $10400
Thus, Amount to be paid = $10400 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) = 10%
And, Time (t) = 10 years
Thus, Amount (A)
= $5200 + ($5200 × 10% × 10)
= $5200 + ($5200 ×10/100 × 10)
= $5200 + (5200 × 10 × 10/100)
= $5200 + (52000 × 10/100)
= $5200 + (520000/100)
= $5200 + $5200 = $10400
Thus, Amount (A) to be paid = $10400 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $5200, the simple interest in 1 year
= 10/100 × 5200
= 10 × 5200/100
= 52000/100 = $520
Thus, simple interest for 1 year = $520
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $520 × 10 = $5200
Thus, Simple Interest (SI) = $5200
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5200 + $5200
= $10400
Thus, Amount to be paid = $10400 Answer
Similar Questions
(1) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.
(2) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $13300 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Mary borrowed a sum of $3050 at 2% simple interest for 3 years.
(4) Calculate the amount due if Thomas borrowed a sum of $3800 at 7% simple interest for 3 years.
(5) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.
(6) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $11200 to clear the loan, then find the time period of the loan.
(7) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 3% simple interest?
(8) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $7360 to clear the loan, then find the time period of the loan.
(9) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $6216 to clear the loan, then find the time period of the loan.
(10) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 7% simple interest?