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) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $6468 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 3% simple interest.
(3) If Matthew paid $5040 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(4) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $7208 to clear the loan, then find the time period of the loan.
(5) John had to pay $3488 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(6) Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $6846 to clear the loan, then find the time period of the loan.
(7) How much loan did Sandra borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7095 to clear it?
(8) What amount does David have to pay after 5 years if he takes a loan of $3400 at 6% simple interest?
(9) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 2% simple interest?
(10) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $9900 to clear the loan, then find the time period of the loan.