Question:
What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 4% simple interest?
Correct Answer
$4140
Solution And Explanation
Solution
Given,
Principal (P) = $3450
Rate of Simple Interest (SI) = 4%
Time (t) = 5 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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 × 4% × 5
= $3450 ×4/100 × 5
= 3450 × 4 × 5/100
= 13800 × 5/100
= 69000/100
= $690
Thus, Simple Interest = $690
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 + $690
= $4140
Thus, Amount to be paid = $4140 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) = 4%
And, Time (t) = 5 years
Thus, Amount (A)
= $3450 + ($3450 × 4% × 5)
= $3450 + ($3450 ×4/100 × 5)
= $3450 + (3450 × 4 × 5/100)
= $3450 + (13800 × 5/100)
= $3450 + (69000/100)
= $3450 + $690 = $4140
Thus, Amount (A) to be paid = $4140 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $3450, the simple interest in 1 year
= 4/100 × 3450
= 4 × 3450/100
= 13800/100 = $138
Thus, simple interest for 1 year = $138
Therefore, simple interest for 5 years
= Simple interest for 1 year × 5
= $138 × 5 = $690
Thus, Simple Interest (SI) = $690
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3450 + $690
= $4140
Thus, Amount to be paid = $4140 Answer
Similar Questions
(1) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $11247 to clear the loan, then find the time period of the loan.
(2) If Charles paid $4368 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(3) Calculate the amount due if Mary borrowed a sum of $3050 at 5% simple interest for 3 years.
(4) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 8% simple interest?
(5) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $11316 to clear the loan, then find the time period of the loan.
(6) If Margaret paid $4698 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(7) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $10000 to clear the loan, then find the time period of the loan.
(8) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $7964 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Thomas borrowed a sum of $3800 at 9% simple interest for 4 years.
(10) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 10% simple interest.