Question:
Calculate the amount due if Elizabeth borrowed a sum of $3450 at 6% simple interest for 3 years.
Correct Answer
$4071
Solution And Explanation
Solution
Given,
Principal (P) = $3450
Rate of Simple Interest (SI) = 6%
Time (t) = 3 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% × 3
= $3450 ×6/100 × 3
= 3450 × 6 × 3/100
= 20700 × 3/100
= 62100/100
= $621
Thus, Simple Interest = $621
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 + $621
= $4071
Thus, Amount to be paid = $4071 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) = 3 years
Thus, Amount (A)
= $3450 + ($3450 × 6% × 3)
= $3450 + ($3450 ×6/100 × 3)
= $3450 + (3450 × 6 × 3/100)
= $3450 + (20700 × 3/100)
= $3450 + (62100/100)
= $3450 + $621 = $4071
Thus, Amount (A) to be paid = $4071 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 3 years
= Simple interest for 1 year × 3
= $207 × 3 = $621
Thus, Simple Interest (SI) = $621
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3450 + $621
= $4071
Thus, Amount to be paid = $4071 Answer
Similar Questions
(1) How much loan did David borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5940 to clear it?
(2) How much loan did Margaret borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6985 to clear it?
(3) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $11160 to clear the loan, then find the time period of the loan.
(4) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $11200 to clear the loan, then find the time period of the loan.
(5) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 9% simple interest?
(6) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $9360 to clear the loan, then find the time period of the loan.
(7) If Patricia borrowed $3150 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(8) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 3% simple interest.
(9) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $10030 to clear the loan, then find the time period of the loan.
(10) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $7100 to clear the loan, then find the time period of the loan.