Question:
Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 6% simple interest.
Correct Answer
$8393
Solution And Explanation
Solution
Given,
Principal (P) = $5450
Rate of Simple Interest (SI) = 6%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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) = $5450 × 6% × 9
= $5450 ×6/100 × 9
= 5450 × 6 × 9/100
= 32700 × 9/100
= 294300/100
= $2943
Thus, Simple Interest = $2943
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 = $5450 + $2943
= $8393
Thus, Amount to be paid = $8393 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 = $5450
Rate of Simple Interest (SI) or (R) = 6%
And, Time (t) = 9 years
Thus, Amount (A)
= $5450 + ($5450 × 6% × 9)
= $5450 + ($5450 ×6/100 × 9)
= $5450 + (5450 × 6 × 9/100)
= $5450 + (32700 × 9/100)
= $5450 + (294300/100)
= $5450 + $2943 = $8393
Thus, Amount (A) to be paid = $8393 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $5450, the simple interest in 1 year
= 6/100 × 5450
= 6 × 5450/100
= 32700/100 = $327
Thus, simple interest for 1 year = $327
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $327 × 9 = $2943
Thus, Simple Interest (SI) = $2943
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5450 + $2943
= $8393
Thus, Amount to be paid = $8393 Answer
Similar Questions
(1) James had to pay $3180 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(2) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 4% simple interest?
(3) In how much time a principal of $3100 will amount to $3348 at a simple interest of 4% per annum?
(4) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $8112 to clear the loan, then find the time period of the loan.
(5) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $10010 to clear the loan, then find the time period of the loan.
(6) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $11352 to clear the loan, then find the time period of the loan.
(7) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $8944 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Jennifer borrowed a sum of $3250 at 10% simple interest for 4 years.
(9) If William paid $4200 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(10) If Thomas paid $4256 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.