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 if John borrowed a sum of $3200 at 7% simple interest for 4 years.
(2) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 3% simple interest.
(3) Find the amount to be paid if Jessica borrowed a sum of $5750 at 3% simple interest for 8 years.
(4) Michael had to pay $3498 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(5) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $9520 to clear the loan, then find the time period of the loan.
(6) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $10240 to clear the loan, then find the time period of the loan.
(7) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 8% simple interest?
(8) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 2% simple interest?
(9) How much loan did Matthew borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7130 to clear it?
(10) What amount does James have to pay after 6 years if he takes a loan of $3000 at 10% simple interest?