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) Patricia had to pay $3339 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(2) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $10370 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 6% simple interest.
(4) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 9% simple interest?
(5) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 9% simple interest.
(6) Mark had to pay $4796 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(7) Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $6552 to clear the loan, then find the time period of the loan.
(8) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 4% simple interest?
(9) Christopher had to pay $4240 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(10) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $12489 to clear the loan, then find the time period of the loan.