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) Calculate the amount due if Joseph borrowed a sum of $3700 at 3% simple interest for 3 years.
(2) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $10240 to clear the loan, then find the time period of the loan.
(3) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 4% simple interest?
(4) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 8% simple interest.
(5) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 2% simple interest.
(6) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 5% simple interest.
(7) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $11008 to clear the loan, then find the time period of the loan.
(8) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 7% simple interest?
(9) Find the amount to be paid if Joseph borrowed a sum of $5700 at 5% simple interest for 7 years.
(10) Find the amount to be paid if Mary borrowed a sum of $5050 at 6% simple interest for 7 years.