Question:
Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 10% simple interest.
Correct Answer
$9500
Solution And Explanation
Solution
Given,
Principal (P) = $5000
Rate of Simple Interest (SI) = 10%
Time (t) = 9 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% × 9
= $5000 ×10/100 × 9
= 5000 × 10 × 9/100
= 50000 × 9/100
= 450000/100
= $4500
Thus, Simple Interest = $4500
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 + $4500
= $9500
Thus, Amount to be paid = $9500 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) = 9 years
Thus, Amount (A)
= $5000 + ($5000 × 10% × 9)
= $5000 + ($5000 ×10/100 × 9)
= $5000 + (5000 × 10 × 9/100)
= $5000 + (50000 × 9/100)
= $5000 + (450000/100)
= $5000 + $4500 = $9500
Thus, Amount (A) to be paid = $9500 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 9 years
= Simple interest for 1 year × 9
= $500 × 9 = $4500
Thus, Simple Interest (SI) = $4500
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5000 + $4500
= $9500
Thus, Amount to be paid = $9500 Answer
Similar Questions
(1) Calculate the amount due if Karen borrowed a sum of $3950 at 3% simple interest for 3 years.
(2) Find the amount to be paid if Linda borrowed a sum of $5350 at 8% simple interest for 8 years.
(3) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $8892 to clear the loan, then find the time period of the loan.
(4) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $11352 to clear the loan, then find the time period of the loan.
(5) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $11220 to clear the loan, then find the time period of the loan.
(6) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 9% simple interest?
(7) Find the amount to be paid if Mary borrowed a sum of $5050 at 3% simple interest for 7 years.
(8) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 3% simple interest?
(9) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 6% simple interest?
(10) Sandra had to pay $5117.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.