Question:
What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 8% simple interest?
Correct Answer
$4830
Solution And Explanation
Solution
Given,
Principal (P) = $3450
Rate of Simple Interest (SI) = 8%
Time (t) = 5 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) = $3450 × 8% × 5
= $3450 ×8/100 × 5
= 3450 × 8 × 5/100
= 27600 × 5/100
= 138000/100
= $1380
Thus, Simple Interest = $1380
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 = $3450 + $1380
= $4830
Thus, Amount to be paid = $4830 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 = $3450
Rate of Simple Interest (SI) or (R) = 8%
And, Time (t) = 5 years
Thus, Amount (A)
= $3450 + ($3450 × 8% × 5)
= $3450 + ($3450 ×8/100 × 5)
= $3450 + (3450 × 8 × 5/100)
= $3450 + (27600 × 5/100)
= $3450 + (138000/100)
= $3450 + $1380 = $4830
Thus, Amount (A) to be paid = $4830 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 $3450, the simple interest in 1 year
= 8/100 × 3450
= 8 × 3450/100
= 27600/100 = $276
Thus, simple interest for 1 year = $276
Therefore, simple interest for 5 years
= Simple interest for 1 year × 5
= $276 × 5 = $1380
Thus, Simple Interest (SI) = $1380
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3450 + $1380
= $4830
Thus, Amount to be paid = $4830 Answer
Similar Questions
(1) Find the amount to be paid if William borrowed a sum of $5500 at 5% simple interest for 7 years.
(2) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 6% simple interest.
(3) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 4% simple interest.
(4) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $11524 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 7% simple interest.
(6) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $13800 to clear the loan, then find the time period of the loan.
(7) Donald had to pay $4770 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(8) Calculate the amount due if David borrowed a sum of $3400 at 8% simple interest for 3 years.
(9) Find the amount to be paid if Michael borrowed a sum of $5300 at 5% simple interest for 8 years.
(10) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 4% simple interest.