Question:
Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 2% simple interest.
Correct Answer
$6240
Solution And Explanation
Solution
Given,
Principal (P) = $5200
Rate of Simple Interest (SI) = 2%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 2% simple interest means, Rate of Simple Interest (SI) is 2% 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 × 2% × 10
= $5200 ×2/100 × 10
= 5200 × 2 × 10/100
= 10400 × 10/100
= 104000/100
= $1040
Thus, Simple Interest = $1040
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 + $1040
= $6240
Thus, Amount to be paid = $6240 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) = 2%
And, Time (t) = 10 years
Thus, Amount (A)
= $5200 + ($5200 × 2% × 10)
= $5200 + ($5200 ×2/100 × 10)
= $5200 + (5200 × 2 × 10/100)
= $5200 + (10400 × 10/100)
= $5200 + (104000/100)
= $5200 + $1040 = $6240
Thus, Amount (A) to be paid = $6240 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 2%
This, means, $2 per $100 per year
∵ For $100, the simple interest for 1 year = $2
∴ For $1, the simple interest for 1 year = 2/100
∴ For $5200, the simple interest in 1 year
= 2/100 × 5200
= 2 × 5200/100
= 10400/100 = $104
Thus, simple interest for 1 year = $104
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $104 × 10 = $1040
Thus, Simple Interest (SI) = $1040
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5200 + $1040
= $6240
Thus, Amount to be paid = $6240 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 8% simple interest.
(2) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 5% simple interest.
(3) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 10% simple interest?
(4) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 6% simple interest?
(5) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7700 to clear the loan, then find the time period of the loan.
(6) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $7344 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 10% simple interest.
(8) Betty had to pay $4632.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(9) Calculate the amount due if David borrowed a sum of $3400 at 3% simple interest for 3 years.
(10) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $6808 to clear the loan, then find the time period of the loan.