Question:
Calculate the amount due if Sarah borrowed a sum of $3850 at 2% simple interest for 3 years.
Correct Answer
$4081
Solution And Explanation
Solution
Given,
Principal (P) = $3850
Rate of Simple Interest (SI) = 2%
Time (t) = 3 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 2% simple interest means, Rate of Simple Interest (SI) is 2% 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 × 2% × 3
= $3850 ×2/100 × 3
= 3850 × 2 × 3/100
= 7700 × 3/100
= 23100/100
= $231
Thus, Simple Interest = $231
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 + $231
= $4081
Thus, Amount to be paid = $4081 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) = 2%
And, Time (t) = 3 years
Thus, Amount (A)
= $3850 + ($3850 × 2% × 3)
= $3850 + ($3850 ×2/100 × 3)
= $3850 + (3850 × 2 × 3/100)
= $3850 + (7700 × 3/100)
= $3850 + (23100/100)
= $3850 + $231 = $4081
Thus, Amount (A) to be paid = $4081 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 2%
This, means, $2 per $100 per year
∵ For $100, the simple interest for 1 year = $2
∴ For $1, the simple interest for 1 year = 2/100
∴ For $3850, the simple interest in 1 year
= 2/100 × 3850
= 2 × 3850/100
= 7700/100 = $77
Thus, simple interest for 1 year = $77
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $77 × 3 = $231
Thus, Simple Interest (SI) = $231
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3850 + $231
= $4081
Thus, Amount to be paid = $4081 Answer
Similar Questions
(1) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 5% simple interest?
(2) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $6256 to clear the loan, then find the time period of the loan.
(3) How much loan did Richard borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6720 to clear it?
(4) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $8280 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 4% simple interest.
(6) How much loan did Michael borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5830 to clear it?
(7) What amount does James have to pay after 6 years if he takes a loan of $3000 at 10% simple interest?
(8) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 4% simple interest?
(9) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $9089 to clear the loan, then find the time period of the loan.
(10) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.