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) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $13200 to clear the loan, then find the time period of the loan.
(2) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $9676 to clear the loan, then find the time period of the loan.
(3) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $7810 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 8% simple interest.
(5) Calculate the amount due if Thomas borrowed a sum of $3800 at 8% simple interest for 4 years.
(6) Find the amount to be paid if Richard borrowed a sum of $5600 at 5% simple interest for 7 years.
(7) Calculate the amount due if Sarah borrowed a sum of $3850 at 3% simple interest for 3 years.
(8) If Donna paid $5238 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(9) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $7400 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if James borrowed a sum of $5000 at 5% simple interest for 8 years.