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) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 5% simple interest?
(2) If Mary paid $3660 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(3) Find the amount to be paid if Karen borrowed a sum of $5950 at 5% simple interest for 8 years.
(4) Find the amount to be paid if James borrowed a sum of $5000 at 6% simple interest for 7 years.
(5) Calculate the amount due if Joseph borrowed a sum of $3700 at 2% simple interest for 3 years.
(6) Calculate the amount due if Patricia borrowed a sum of $3150 at 4% simple interest for 4 years.
(7) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $9310 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 10% simple interest.
(9) Calculate the amount due if Linda borrowed a sum of $3350 at 10% simple interest for 4 years.
(10) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $8778 to clear the loan, then find the time period of the loan.