Question:
Find the amount to be paid if Sarah borrowed a sum of $5850 at 2% simple interest for 8 years.
Correct Answer
$6786
Solution And Explanation
Solution
Given,
Principal (P) = $5850
Rate of Simple Interest (SI) = 2%
Time (t) = 8 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) = $5850 × 2% × 8
= $5850 ×2/100 × 8
= 5850 × 2 × 8/100
= 11700 × 8/100
= 93600/100
= $936
Thus, Simple Interest = $936
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 = $5850 + $936
= $6786
Thus, Amount to be paid = $6786 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 = $5850
Rate of Simple Interest (SI) or (R) = 2%
And, Time (t) = 8 years
Thus, Amount (A)
= $5850 + ($5850 × 2% × 8)
= $5850 + ($5850 ×2/100 × 8)
= $5850 + (5850 × 2 × 8/100)
= $5850 + (11700 × 8/100)
= $5850 + (93600/100)
= $5850 + $936 = $6786
Thus, Amount (A) to be paid = $6786 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 $5850, the simple interest in 1 year
= 2/100 × 5850
= 2 × 5850/100
= 11700/100 = $117
Thus, simple interest for 1 year = $117
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $117 × 8 = $936
Thus, Simple Interest (SI) = $936
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5850 + $936
= $6786
Thus, Amount to be paid = $6786 Answer
Similar Questions
(1) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10004 to clear the loan, then find the time period of the loan.
(2) If Donna paid $5820 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(3) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $6864 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Linda borrowed a sum of $5350 at 2% simple interest for 7 years.
(5) Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $8584 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if David borrowed a sum of $5400 at 6% simple interest for 7 years.
(7) Calculate the amount due if Joseph borrowed a sum of $3700 at 9% simple interest for 3 years.
(8) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $11524 to clear the loan, then find the time period of the loan.
(9) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9060 to clear it?
(10) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $7920 to clear the loan, then find the time period of the loan.