Question:
Find the amount to be paid if James borrowed a sum of $5000 at 10% simple interest for 7 years.
Correct Answer
$8500
Solution And Explanation
Solution
Given,
Principal (P) = $5000
Rate of Simple Interest (SI) = 10%
Time (t) = 7 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) = $5000 × 10% × 7
= $5000 ×10/100 × 7
= 5000 × 10 × 7/100
= 50000 × 7/100
= 350000/100
= $3500
Thus, Simple Interest = $3500
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 = $5000 + $3500
= $8500
Thus, Amount to be paid = $8500 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 = $5000
Rate of Simple Interest (SI) or (R) = 10%
And, Time (t) = 7 years
Thus, Amount (A)
= $5000 + ($5000 × 10% × 7)
= $5000 + ($5000 ×10/100 × 7)
= $5000 + (5000 × 10 × 7/100)
= $5000 + (50000 × 7/100)
= $5000 + (350000/100)
= $5000 + $3500 = $8500
Thus, Amount (A) to be paid = $8500 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 $5000, the simple interest in 1 year
= 10/100 × 5000
= 10 × 5000/100
= 50000/100 = $500
Thus, simple interest for 1 year = $500
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $500 × 7 = $3500
Thus, Simple Interest (SI) = $3500
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5000 + $3500
= $8500
Thus, Amount to be paid = $8500 Answer
Similar Questions
(1) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 4% simple interest?
(2) Daniel had to pay $4715 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(3) Charles had to pay $4368 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(4) John had to pay $3584 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(5) David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $6816 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 9% simple interest.
(7) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $8662 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 8% simple interest.
(9) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 10% simple interest.
(10) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 7% simple interest.