Question:
Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 5% simple interest.
Correct Answer
$7800
Solution And Explanation
Solution
Given,
Principal (P) = $5200
Rate of Simple Interest (SI) = 5%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 10
= $5200 ×5/100 × 10
= 5200 × 5 × 10/100
= 26000 × 10/100
= 260000/100
= $2600
Thus, Simple Interest = $2600
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 + $2600
= $7800
Thus, Amount to be paid = $7800 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) = 5%
And, Time (t) = 10 years
Thus, Amount (A)
= $5200 + ($5200 × 5% × 10)
= $5200 + ($5200 ×5/100 × 10)
= $5200 + (5200 × 5 × 10/100)
= $5200 + (26000 × 10/100)
= $5200 + (260000/100)
= $5200 + $2600 = $7800
Thus, Amount (A) to be paid = $7800 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $5200, the simple interest in 1 year
= 5/100 × 5200
= 5 × 5200/100
= 26000/100 = $260
Thus, simple interest for 1 year = $260
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $260 × 10 = $2600
Thus, Simple Interest (SI) = $2600
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5200 + $2600
= $7800
Thus, Amount to be paid = $7800 Answer
Similar Questions
(1) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 5% simple interest.
(2) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 7% simple interest?
(3) If Robert borrowed $3100 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(4) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $10758 to clear the loan, then find the time period of the loan.
(5) How much loan did Mark borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8000 to clear it?
(6) What amount will be due after 2 years if John borrowed a sum of $3100 at a 5% simple interest?
(7) Matthew had to pay $4578 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(8) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $9900 to clear the loan, then find the time period of the loan.
(9) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $10764 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 6% simple interest.