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) How much loan did Robert borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6120 to clear it?
(2) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $8296 to clear the loan, then find the time period of the loan.
(3) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $9088 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Sarah borrowed a sum of $5850 at 10% simple interest for 8 years.
(5) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 7% simple interest.
(6) Find the amount to be paid if Linda borrowed a sum of $5350 at 6% simple interest for 8 years.
(7) If Kimberly paid $5022 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(8) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $8976 to clear the loan, then find the time period of the loan.
(9) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 10% simple interest?
(10) How much loan did Mary borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5807.5 to clear it?