Question:
Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 2% simple interest.
Correct Answer
$6667
Solution And Explanation
Solution
Given,
Principal (P) = $5650
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) = $5650 × 2% × 9
= $5650 ×2/100 × 9
= 5650 × 2 × 9/100
= 11300 × 9/100
= 101700/100
= $1017
Thus, Simple Interest = $1017
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 = $5650 + $1017
= $6667
Thus, Amount to be paid = $6667 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 = $5650
Rate of Simple Interest (SI) or (R) = 2%
And, Time (t) = 9 years
Thus, Amount (A)
= $5650 + ($5650 × 2% × 9)
= $5650 + ($5650 ×2/100 × 9)
= $5650 + (5650 × 2 × 9/100)
= $5650 + (11300 × 9/100)
= $5650 + (101700/100)
= $5650 + $1017 = $6667
Thus, Amount (A) to be paid = $6667 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 $5650, the simple interest in 1 year
= 2/100 × 5650
= 2 × 5650/100
= 11300/100 = $113
Thus, simple interest for 1 year = $113
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $113 × 9 = $1017
Thus, Simple Interest (SI) = $1017
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5650 + $1017
= $6667
Thus, Amount to be paid = $6667 Answer
Similar Questions
(1) In how much time a principal of $3200 will amount to $3392 at a simple interest of 2% per annum?
(2) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $11400 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 10% simple interest for 8 years.
(4) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $7992 to clear the loan, then find the time period of the loan.
(5) How much loan did James borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5500 to clear it?
(6) Calculate the amount due if Susan borrowed a sum of $3650 at 7% simple interest for 3 years.
(7) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 5% simple interest.
(8) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 5% simple interest.
(9) If Karen paid $4424 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(10) Find the amount to be paid if Mary borrowed a sum of $5050 at 6% simple interest for 7 years.