Question:
Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 2% simple interest.
Correct Answer
$6903
Solution And Explanation
Solution
Given,
Principal (P) = $5850
Rate of Simple Interest (SI) = 2%
Time (t) = 9 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% × 9
= $5850 ×2/100 × 9
= 5850 × 2 × 9/100
= 11700 × 9/100
= 105300/100
= $1053
Thus, Simple Interest = $1053
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 + $1053
= $6903
Thus, Amount to be paid = $6903 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) = 9 years
Thus, Amount (A)
= $5850 + ($5850 × 2% × 9)
= $5850 + ($5850 ×2/100 × 9)
= $5850 + (5850 × 2 × 9/100)
= $5850 + (11700 × 9/100)
= $5850 + (105300/100)
= $5850 + $1053 = $6903
Thus, Amount (A) to be paid = $6903 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 9 years
= Simple interest for 1 year × 9
= $117 × 9 = $1053
Thus, Simple Interest (SI) = $1053
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5850 + $1053
= $6903
Thus, Amount to be paid = $6903 Answer
Similar Questions
(1) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $9983 to clear the loan, then find the time period of the loan.
(2) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $10136 to clear the loan, then find the time period of the loan.
(3) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $6930 to clear the loan, then find the time period of the loan.
(4) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $10608 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 5% simple interest.
(6) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 10% simple interest.
(7) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 10% simple interest?
(8) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 5% simple interest.
(9) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 2% simple interest.
(10) Calculate the amount due if Thomas borrowed a sum of $3800 at 2% simple interest for 3 years.