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) Robert had to pay $3565 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(2) Find the amount to be paid if Patricia borrowed a sum of $5150 at 8% simple interest for 7 years.
(3) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 4% simple interest.
(4) Find the amount to be paid if Karen borrowed a sum of $5950 at 8% simple interest for 8 years.
(5) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $7380 to clear the loan, then find the time period of the loan.
(6) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 7% simple interest?
(7) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $11524 to clear the loan, then find the time period of the loan.
(8) How much loan did Margaret borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6985 to clear it?
(9) Find the amount to be paid if Christopher borrowed a sum of $6000 at 4% simple interest for 8 years.
(10) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $7820 to clear the loan, then find the time period of the loan.