Question:
Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 4% simple interest.
Correct Answer
$7630
Solution And Explanation
Solution
Given,
Principal (P) = $5450
Rate of Simple Interest (SI) = 4%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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 × 4% × 10
= $5450 ×4/100 × 10
= 5450 × 4 × 10/100
= 21800 × 10/100
= 218000/100
= $2180
Thus, Simple Interest = $2180
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 + $2180
= $7630
Thus, Amount to be paid = $7630 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) = 4%
And, Time (t) = 10 years
Thus, Amount (A)
= $5450 + ($5450 × 4% × 10)
= $5450 + ($5450 ×4/100 × 10)
= $5450 + (5450 × 4 × 10/100)
= $5450 + (21800 × 10/100)
= $5450 + (218000/100)
= $5450 + $2180 = $7630
Thus, Amount (A) to be paid = $7630 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $5450, the simple interest in 1 year
= 4/100 × 5450
= 4 × 5450/100
= 21800/100 = $218
Thus, simple interest for 1 year = $218
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $218 × 10 = $2180
Thus, Simple Interest (SI) = $2180
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5450 + $2180
= $7630
Thus, Amount to be paid = $7630 Answer
Similar Questions
(1) Find the amount to be paid if William borrowed a sum of $5500 at 3% simple interest for 8 years.
(2) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 9% simple interest?
(3) How much loan did Mary borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6060 to clear it?
(4) If Paul paid $5076 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(5) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $5920 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Jessica borrowed a sum of $5750 at 6% simple interest for 7 years.
(7) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $9050 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 7% simple interest.
(9) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $10452 to clear the loan, then find the time period of the loan.
(10) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $10064 to clear the loan, then find the time period of the loan.