Question:
Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 5% simple interest.
Correct Answer
$7540
Solution And Explanation
Solution
Given,
Principal (P) = $5200
Rate of Simple Interest (SI) = 5%
Time (t) = 9 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% × 9
= $5200 ×5/100 × 9
= 5200 × 5 × 9/100
= 26000 × 9/100
= 234000/100
= $2340
Thus, Simple Interest = $2340
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 + $2340
= $7540
Thus, Amount to be paid = $7540 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) = 9 years
Thus, Amount (A)
= $5200 + ($5200 × 5% × 9)
= $5200 + ($5200 ×5/100 × 9)
= $5200 + (5200 × 5 × 9/100)
= $5200 + (26000 × 9/100)
= $5200 + (234000/100)
= $5200 + $2340 = $7540
Thus, Amount (A) to be paid = $7540 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 9 years
= Simple interest for 1 year × 9
= $260 × 9 = $2340
Thus, Simple Interest (SI) = $2340
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5200 + $2340
= $7540
Thus, Amount to be paid = $7540 Answer
Similar Questions
(1) If Richard borrowed $3600 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(2) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $11780 to clear the loan, then find the time period of the loan.
(3) Richard had to pay $4140 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(4) In how much time a principal of $3100 will amount to $3565 at a simple interest of 5% per annum?
(5) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 2% simple interest?
(6) Charles had to pay $4485 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(7) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 6% simple interest.
(8) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 3% simple interest?
(9) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $10920 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Joseph borrowed a sum of $3700 at 9% simple interest for 4 years.