Question:
Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 8% simple interest for 8 years.
Correct Answer
$8938
Solution And Explanation
Solution
Given,
Principal (P) = $5450
Rate of Simple Interest (SI) = 8%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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 × 8% × 8
= $5450 ×8/100 × 8
= 5450 × 8 × 8/100
= 43600 × 8/100
= 348800/100
= $3488
Thus, Simple Interest = $3488
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 + $3488
= $8938
Thus, Amount to be paid = $8938 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) = 8%
And, Time (t) = 8 years
Thus, Amount (A)
= $5450 + ($5450 × 8% × 8)
= $5450 + ($5450 ×8/100 × 8)
= $5450 + (5450 × 8 × 8/100)
= $5450 + (43600 × 8/100)
= $5450 + (348800/100)
= $5450 + $3488 = $8938
Thus, Amount (A) to be paid = $8938 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $5450, the simple interest in 1 year
= 8/100 × 5450
= 8 × 5450/100
= 43600/100 = $436
Thus, simple interest for 1 year = $436
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $436 × 8 = $3488
Thus, Simple Interest (SI) = $3488
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5450 + $3488
= $8938
Thus, Amount to be paid = $8938 Answer
Similar Questions
(1) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $8580 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 6% simple interest.
(3) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 7% simple interest?
(4) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $11946 to clear the loan, then find the time period of the loan.
(5) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6660 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if David borrowed a sum of $5400 at 6% simple interest for 7 years.
(7) What amount does David have to pay after 6 years if he takes a loan of $3400 at 3% simple interest?
(8) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $8662 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 6% simple interest.
(10) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $8200 to clear the loan, then find the time period of the loan.