Question:
Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 6% simple interest.
Correct Answer
$7700
Solution And Explanation
Solution
Given,
Principal (P) = $5000
Rate of Simple Interest (SI) = 6%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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 × 6% × 9
= $5000 ×6/100 × 9
= 5000 × 6 × 9/100
= 30000 × 9/100
= 270000/100
= $2700
Thus, Simple Interest = $2700
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 + $2700
= $7700
Thus, Amount to be paid = $7700 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) = 6%
And, Time (t) = 9 years
Thus, Amount (A)
= $5000 + ($5000 × 6% × 9)
= $5000 + ($5000 ×6/100 × 9)
= $5000 + (5000 × 6 × 9/100)
= $5000 + (30000 × 9/100)
= $5000 + (270000/100)
= $5000 + $2700 = $7700
Thus, Amount (A) to be paid = $7700 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $5000, the simple interest in 1 year
= 6/100 × 5000
= 6 × 5000/100
= 30000/100 = $300
Thus, simple interest for 1 year = $300
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $300 × 9 = $2700
Thus, Simple Interest (SI) = $2700
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5000 + $2700
= $7700
Thus, Amount to be paid = $7700 Answer
Similar Questions
(1) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $9310 to clear the loan, then find the time period of the loan.
(2) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 10% simple interest?
(3) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 4% simple interest?
(4) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $7920 to clear the loan, then find the time period of the loan.
(5) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $9088 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Charles borrowed a sum of $3900 at 4% simple interest for 4 years.
(7) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $9600 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Karen borrowed a sum of $3950 at 4% simple interest for 4 years.
(9) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 8% simple interest.
(10) Calculate the amount due if Richard borrowed a sum of $3600 at 8% simple interest for 3 years.