Question:
What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 7% simple interest?
Correct Answer
$5680
Solution And Explanation
Solution
Given,
Principal (P) = $4000
Rate of Simple Interest (SI) = 7%
Time (t) = 6 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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) = $4000 × 7% × 6
= $4000 ×7/100 × 6
= 4000 × 7 × 6/100
= 28000 × 6/100
= 168000/100
= $1680
Thus, Simple Interest = $1680
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 = $4000 + $1680
= $5680
Thus, Amount to be paid = $5680 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 = $4000
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 6 years
Thus, Amount (A)
= $4000 + ($4000 × 7% × 6)
= $4000 + ($4000 ×7/100 × 6)
= $4000 + (4000 × 7 × 6/100)
= $4000 + (28000 × 6/100)
= $4000 + (168000/100)
= $4000 + $1680 = $5680
Thus, Amount (A) to be paid = $5680 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $4000, the simple interest in 1 year
= 7/100 × 4000
= 7 × 4000/100
= 28000/100 = $280
Thus, simple interest for 1 year = $280
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $280 × 6 = $1680
Thus, Simple Interest (SI) = $1680
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $4000 + $1680
= $5680
Thus, Amount to be paid = $5680 Answer
Similar Questions
(1) Find the amount to be paid if James borrowed a sum of $5000 at 2% simple interest for 7 years.
(2) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 2% simple interest for 7 years.
(3) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $7783 to clear the loan, then find the time period of the loan.
(4) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 3% simple interest?
(5) What amount does James have to pay after 6 years if he takes a loan of $3000 at 7% simple interest?
(6) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 7% simple interest.
(7) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $8288 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 10% simple interest.
(9) Susan had to pay $4088 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(10) How much loan did Thomas borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6380 to clear it?