Question:
Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 5% simple interest.
Correct Answer
$8700
Solution And Explanation
Solution
Given,
Principal (P) = $6000
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) = $6000 × 5% × 9
= $6000 ×5/100 × 9
= 6000 × 5 × 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 = $6000 + $2700
= $8700
Thus, Amount to be paid = $8700 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 = $6000
Rate of Simple Interest (SI) or (R) = 5%
And, Time (t) = 9 years
Thus, Amount (A)
= $6000 + ($6000 × 5% × 9)
= $6000 + ($6000 ×5/100 × 9)
= $6000 + (6000 × 5 × 9/100)
= $6000 + (30000 × 9/100)
= $6000 + (270000/100)
= $6000 + $2700 = $8700
Thus, Amount (A) to be paid = $8700 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 $6000, the simple interest in 1 year
= 5/100 × 6000
= 5 × 6000/100
= 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 = $6000 + $2700
= $8700
Thus, Amount to be paid = $8700 Answer
Similar Questions
(1) Calculate the amount due if David borrowed a sum of $3400 at 3% simple interest for 4 years.
(2) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 2% simple interest?
(3) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 10% simple interest?
(4) How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9750 to clear it?
(5) Calculate the amount due if David borrowed a sum of $3400 at 4% simple interest for 4 years.
(6) Find the amount to be paid if David borrowed a sum of $5400 at 7% simple interest for 7 years.
(7) Calculate the amount due if Jessica borrowed a sum of $3750 at 10% simple interest for 4 years.
(8) How much loan did George borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8760 to clear it?
(9) James had to pay $3270 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(10) What amount does James have to pay after 6 years if he takes a loan of $3000 at 7% simple interest?