Question:
Calculate the amount due if Sarah borrowed a sum of $3850 at 2% simple interest for 4 years.
Correct Answer
$4158
Solution And Explanation
Solution
Given,
Principal (P) = $3850
Rate of Simple Interest (SI) = 2%
Time (t) = 4 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% × 4
= $3850 ×2/100 × 4
= 3850 × 2 × 4/100
= 7700 × 4/100
= 30800/100
= $308
Thus, Simple Interest = $308
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 + $308
= $4158
Thus, Amount to be paid = $4158 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) = 4 years
Thus, Amount (A)
= $3850 + ($3850 × 2% × 4)
= $3850 + ($3850 ×2/100 × 4)
= $3850 + (3850 × 2 × 4/100)
= $3850 + (7700 × 4/100)
= $3850 + (30800/100)
= $3850 + $308 = $4158
Thus, Amount (A) to be paid = $4158 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 4 years
= Simple interest for 1 year × 4
= $77 × 4 = $308
Thus, Simple Interest (SI) = $308
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3850 + $308
= $4158
Thus, Amount to be paid = $4158 Answer
Similar Questions
(1) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $7052 to clear the loan, then find the time period of the loan.
(2) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 8% simple interest?
(3) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 3% simple interest?
(4) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 9% simple interest?
(5) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $7344 to clear the loan, then find the time period of the loan.
(6) If Barbara paid $4260 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(7) If Joshua paid $5488 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(8) Calculate the amount due if James borrowed a sum of $3000 at 5% simple interest for 4 years.
(9) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $10830 to clear the loan, then find the time period of the loan.
(10) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $9384 to clear the loan, then find the time period of the loan.