Question:
What amount does William have to pay after 6 years if he takes a loan of $3500 at 7% simple interest?
Correct Answer
$4970
Solution And Explanation
Solution
Given,
Principal (P) = $3500
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) = $3500 × 7% × 6
= $3500 ×7/100 × 6
= 3500 × 7 × 6/100
= 24500 × 6/100
= 147000/100
= $1470
Thus, Simple Interest = $1470
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 = $3500 + $1470
= $4970
Thus, Amount to be paid = $4970 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 = $3500
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 6 years
Thus, Amount (A)
= $3500 + ($3500 × 7% × 6)
= $3500 + ($3500 ×7/100 × 6)
= $3500 + (3500 × 7 × 6/100)
= $3500 + (24500 × 6/100)
= $3500 + (147000/100)
= $3500 + $1470 = $4970
Thus, Amount (A) to be paid = $4970 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 $3500, the simple interest in 1 year
= 7/100 × 3500
= 7 × 3500/100
= 24500/100 = $245
Thus, simple interest for 1 year = $245
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $245 × 6 = $1470
Thus, Simple Interest (SI) = $1470
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3500 + $1470
= $4970
Thus, Amount to be paid = $4970 Answer
Similar Questions
(1) Find the amount to be paid if Michael borrowed a sum of $5300 at 5% simple interest for 7 years.
(2) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $7992 to clear the loan, then find the time period of the loan.
(3) 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.
(4) Find the amount to be paid if Linda borrowed a sum of $5350 at 4% simple interest for 7 years.
(5) Find the amount to be paid if Robert borrowed a sum of $5100 at 7% simple interest for 7 years.
(6) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $8094 to clear the loan, then find the time period of the loan.
(7) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 9% simple interest?
(8) How much loan did Jessica borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7187.5 to clear it?
(9) Donna had to pay $5286.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(10) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $9086 to clear the loan, then find the time period of the loan.