Question:
Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 7% simple interest for 8 years.
Correct Answer
$8502
Solution And Explanation
Solution
Given,
Principal (P) = $5450
Rate of Simple Interest (SI) = 7%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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 × 7% × 8
= $5450 ×7/100 × 8
= 5450 × 7 × 8/100
= 38150 × 8/100
= 305200/100
= $3052
Thus, Simple Interest = $3052
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 + $3052
= $8502
Thus, Amount to be paid = $8502 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) = 7%
And, Time (t) = 8 years
Thus, Amount (A)
= $5450 + ($5450 × 7% × 8)
= $5450 + ($5450 ×7/100 × 8)
= $5450 + (5450 × 7 × 8/100)
= $5450 + (38150 × 8/100)
= $5450 + (305200/100)
= $5450 + $3052 = $8502
Thus, Amount (A) to be paid = $8502 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $5450, the simple interest in 1 year
= 7/100 × 5450
= 7 × 5450/100
= 38150/100 = $381.5
Thus, simple interest for 1 year = $381.5
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $381.5 × 8 = $3052
Thus, Simple Interest (SI) = $3052
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5450 + $3052
= $8502
Thus, Amount to be paid = $8502 Answer
Similar Questions
(1) How much loan did Michael borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6095 to clear it?
(2) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $7650 to clear the loan, then find the time period of the loan.
(3) What amount does William have to pay after 6 years if he takes a loan of $3500 at 4% simple interest?
(4) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 10% simple interest?
(5) In how much time a principal of $3150 will amount to $3402 at a simple interest of 2% per annum?
(6) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 5% simple interest.
(7) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $10450 to clear the loan, then find the time period of the loan.
(8) Christopher had to pay $4360 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(9) Sandra had to pay $5117.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(10) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 10% simple interest.