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) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 3% simple interest?
(2) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $9632 to clear the loan, then find the time period of the loan.
(3) If Michael paid $3960 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(4) In how much time a principal of $3050 will amount to $3355 at a simple interest of 5% per annum?
(5) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $9593 to clear the loan, then find the time period of the loan.
(6) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $8288 to clear the loan, then find the time period of the loan.
(7) Karen had to pay $4542.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(8) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 10% simple interest?
(9) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $10136 to clear the loan, then find the time period of the loan.
(10) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.