Question:
Calculate the amount due if Elizabeth borrowed a sum of $3450 at 5% simple interest for 4 years.
Correct Answer
$4140
Solution And Explanation
Solution
Given,
Principal (P) = $3450
Rate of Simple Interest (SI) = 5%
Time (t) = 4 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 4
= $3450 ×5/100 × 4
= 3450 × 5 × 4/100
= 17250 × 4/100
= 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) = 5%
And, Time (t) = 4 years
Thus, Amount (A)
= $3450 + ($3450 × 5% × 4)
= $3450 + ($3450 ×5/100 × 4)
= $3450 + (3450 × 5 × 4/100)
= $3450 + (17250 × 4/100)
= $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 = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $3450, the simple interest in 1 year
= 5/100 × 3450
= 5 × 3450/100
= 17250/100 = $172.5
Thus, simple interest for 1 year = $172.5
Therefore, simple interest for 4 years
= Simple interest for 1 year × 4
= $172.5 × 4 = $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) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $8662 to clear the loan, then find the time period of the loan.
(2) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $10560 to clear the loan, then find the time period of the loan.
(3) 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.
(4) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 9% simple interest?
(5) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $8624 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Barbara borrowed a sum of $5550 at 5% simple interest for 8 years.
(7) How much loan did Brian borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9000 to clear it?
(8) In how much time a principal of $3050 will amount to $3660 at a simple interest of 4% per annum?
(9) Find the amount to be paid if Thomas borrowed a sum of $5800 at 5% simple interest for 8 years.
(10) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $7568 to clear the loan, then find the time period of the loan.