Question:
Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 5% simple interest for 8 years.
Correct Answer
$7630
Solution And Explanation
Solution
Given,
Principal (P) = $5450
Rate of Simple Interest (SI) = 5%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 8
= $5450 ×5/100 × 8
= 5450 × 5 × 8/100
= 27250 × 8/100
= 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) = 5%
And, Time (t) = 8 years
Thus, Amount (A)
= $5450 + ($5450 × 5% × 8)
= $5450 + ($5450 ×5/100 × 8)
= $5450 + (5450 × 5 × 8/100)
= $5450 + (27250 × 8/100)
= $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 = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $5450, the simple interest in 1 year
= 5/100 × 5450
= 5 × 5450/100
= 27250/100 = $272.5
Thus, simple interest for 1 year = $272.5
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $272.5 × 8 = $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) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 8% simple interest?
(2) Find the amount to be paid if Christopher borrowed a sum of $6000 at 2% simple interest for 8 years.
(3) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 4% simple interest?
(4) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $7920 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 5% simple interest.
(6) Find the amount to be paid if Linda borrowed a sum of $5350 at 8% simple interest for 8 years.
(7) Lisa had to pay $4536 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(8) In how much time a principal of $3100 will amount to $3286 at a simple interest of 3% per annum?
(9) Calculate the amount due if Sarah borrowed a sum of $3850 at 7% simple interest for 3 years.
(10) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $10560 to clear the loan, then find the time period of the loan.