Question:
Calculate the amount due if Sarah borrowed a sum of $3850 at 10% simple interest for 4 years.
Correct Answer
$5390
Solution And Explanation
Solution
Given,
Principal (P) = $3850
Rate of Simple Interest (SI) = 10%
Time (t) = 4 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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) = $3850 × 10% × 4
= $3850 ×10/100 × 4
= 3850 × 10 × 4/100
= 38500 × 4/100
= 154000/100
= $1540
Thus, Simple Interest = $1540
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 = $3850 + $1540
= $5390
Thus, Amount to be paid = $5390 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 = $3850
Rate of Simple Interest (SI) or (R) = 10%
And, Time (t) = 4 years
Thus, Amount (A)
= $3850 + ($3850 × 10% × 4)
= $3850 + ($3850 ×10/100 × 4)
= $3850 + (3850 × 10 × 4/100)
= $3850 + (38500 × 4/100)
= $3850 + (154000/100)
= $3850 + $1540 = $5390
Thus, Amount (A) to be paid = $5390 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $3850, the simple interest in 1 year
= 10/100 × 3850
= 10 × 3850/100
= 38500/100 = $385
Thus, simple interest for 1 year = $385
Therefore, simple interest for 4 years
= Simple interest for 1 year × 4
= $385 × 4 = $1540
Thus, Simple Interest (SI) = $1540
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3850 + $1540
= $5390
Thus, Amount to be paid = $5390 Answer
Similar Questions
(1) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $9516 to clear the loan, then find the time period of the loan.
(2) Lisa had to pay $4414.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(3) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $8932 to clear the loan, then find the time period of the loan.
(4) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8797.5 to clear it?
(5) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 8% simple interest.
(6) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $7240 to clear the loan, then find the time period of the loan.
(7) What amount does William have to pay after 5 years if he takes a loan of $3500 at 3% simple interest?
(8) How much loan did Anthony borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7560 to clear it?
(9) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $7992 to clear the loan, then find the time period of the loan.
(10) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $6512 to clear the loan, then find the time period of the loan.