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) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9142.5 to clear it?
(2) How much loan did Donna borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7877.5 to clear it?
(3) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.
(4) Elizabeth had to pay $3760.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(5) If Mark paid $4928 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(6) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $8791 to clear the loan, then find the time period of the loan.
(7) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 8% simple interest?
(8) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 2% simple interest?
(9) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $11180 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if Mary borrowed a sum of $5050 at 2% simple interest for 7 years.