Question:
Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 6% simple interest for 8 years.
Correct Answer
$8066
Solution And Explanation
Solution
Given,
Principal (P) = $5450
Rate of Simple Interest (SI) = 6%
Time (t) = 8 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% × 8
= $5450 ×6/100 × 8
= 5450 × 6 × 8/100
= 32700 × 8/100
= 261600/100
= $2616
Thus, Simple Interest = $2616
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 + $2616
= $8066
Thus, Amount to be paid = $8066 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) = 8 years
Thus, Amount (A)
= $5450 + ($5450 × 6% × 8)
= $5450 + ($5450 ×6/100 × 8)
= $5450 + (5450 × 6 × 8/100)
= $5450 + (32700 × 8/100)
= $5450 + (261600/100)
= $5450 + $2616 = $8066
Thus, Amount (A) to be paid = $8066 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 8 years
= Simple interest for 1 year × 8
= $327 × 8 = $2616
Thus, Simple Interest (SI) = $2616
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5450 + $2616
= $8066
Thus, Amount to be paid = $8066 Answer
Similar Questions
(1) Thomas had to pay $4256 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(2) What amount does John have to pay after 6 years if he takes a loan of $3200 at 3% simple interest?
(3) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $9500 to clear the loan, then find the time period of the loan.
(4) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 2% simple interest?
(5) How much loan did Ronald borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9000 to clear it?
(6) Find the amount to be paid if William borrowed a sum of $5500 at 7% simple interest for 7 years.
(7) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 4% simple interest?
(8) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $9620 to clear the loan, then find the time period of the loan.
(9) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 3% simple interest?
(10) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 5% simple interest.