Question:
What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 7% simple interest?
Correct Answer
$5609
Solution And Explanation
Solution
Given,
Principal (P) = $3950
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) = $3950 × 7% × 6
= $3950 ×7/100 × 6
= 3950 × 7 × 6/100
= 27650 × 6/100
= 165900/100
= $1659
Thus, Simple Interest = $1659
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 = $3950 + $1659
= $5609
Thus, Amount to be paid = $5609 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 = $3950
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 6 years
Thus, Amount (A)
= $3950 + ($3950 × 7% × 6)
= $3950 + ($3950 ×7/100 × 6)
= $3950 + (3950 × 7 × 6/100)
= $3950 + (27650 × 6/100)
= $3950 + (165900/100)
= $3950 + $1659 = $5609
Thus, Amount (A) to be paid = $5609 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 $3950, the simple interest in 1 year
= 7/100 × 3950
= 7 × 3950/100
= 27650/100 = $276.5
Thus, simple interest for 1 year = $276.5
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $276.5 × 6 = $1659
Thus, Simple Interest (SI) = $1659
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3950 + $1659
= $5609
Thus, Amount to be paid = $5609 Answer
Similar Questions
(1) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 4% simple interest?
(2) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 2% simple interest.
(3) Calculate the amount due if Michael borrowed a sum of $3300 at 10% simple interest for 3 years.
(4) Charles had to pay $4485 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(5) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 6% simple interest.
(6) John had to pay $3680 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(7) Calculate the amount due if David borrowed a sum of $3400 at 3% simple interest for 3 years.
(8) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $8162 to clear the loan, then find the time period of the loan.
(9) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $7668 to clear the loan, then find the time period of the loan.
(10) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 9% simple interest?