Question:
Calculate the amount due if Elizabeth borrowed a sum of $3450 at 6% simple interest for 4 years.
Correct Answer
$4278
Solution And Explanation
Solution
Given,
Principal (P) = $3450
Rate of Simple Interest (SI) = 6%
Time (t) = 4 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) = $3450 × 6% × 4
= $3450 ×6/100 × 4
= 3450 × 6 × 4/100
= 20700 × 4/100
= 82800/100
= $828
Thus, Simple Interest = $828
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 + $828
= $4278
Thus, Amount to be paid = $4278 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) = 6%
And, Time (t) = 4 years
Thus, Amount (A)
= $3450 + ($3450 × 6% × 4)
= $3450 + ($3450 ×6/100 × 4)
= $3450 + (3450 × 6 × 4/100)
= $3450 + (20700 × 4/100)
= $3450 + (82800/100)
= $3450 + $828 = $4278
Thus, Amount (A) to be paid = $4278 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 $3450, the simple interest in 1 year
= 6/100 × 3450
= 6 × 3450/100
= 20700/100 = $207
Thus, simple interest for 1 year = $207
Therefore, simple interest for 4 years
= Simple interest for 1 year × 4
= $207 × 4 = $828
Thus, Simple Interest (SI) = $828
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3450 + $828
= $4278
Thus, Amount to be paid = $4278 Answer
Similar Questions
(1) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $8436 to clear the loan, then find the time period of the loan.
(2) 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.
(3) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $9128 to clear the loan, then find the time period of the loan.
(4) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $7840 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Mary borrowed a sum of $5050 at 5% simple interest for 7 years.
(6) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 4% simple interest.
(7) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 6% simple interest.
(8) Calculate the amount due if Sarah borrowed a sum of $3850 at 10% simple interest for 4 years.
(9) In how much time a principal of $3150 will amount to $3780 at a simple interest of 5% per annum?
(10) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 3% simple interest.