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) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 8% simple interest?
(2) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $7040 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Thomas borrowed a sum of $5800 at 5% simple interest for 8 years.
(4) What amount does John have to pay after 5 years if he takes a loan of $3200 at 3% simple interest?
(5) What amount does David have to pay after 6 years if he takes a loan of $3400 at 10% simple interest?
(6) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $11560 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 6% simple interest.
(8) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $5964 to clear the loan, then find the time period of the loan.
(9) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $7650 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 9% simple interest.