Question:
Calculate the amount due if Elizabeth borrowed a sum of $3450 at 10% simple interest for 3 years.
Correct Answer
$4485
Solution And Explanation
Solution
Given,
Principal (P) = $3450
Rate of Simple Interest (SI) = 10%
Time (t) = 3 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 3
= $3450 ×10/100 × 3
= 3450 × 10 × 3/100
= 34500 × 3/100
= 103500/100
= $1035
Thus, Simple Interest = $1035
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 + $1035
= $4485
Thus, Amount to be paid = $4485 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) = 10%
And, Time (t) = 3 years
Thus, Amount (A)
= $3450 + ($3450 × 10% × 3)
= $3450 + ($3450 ×10/100 × 3)
= $3450 + (3450 × 10 × 3/100)
= $3450 + (34500 × 3/100)
= $3450 + (103500/100)
= $3450 + $1035 = $4485
Thus, Amount (A) to be paid = $4485 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $3450, the simple interest in 1 year
= 10/100 × 3450
= 10 × 3450/100
= 34500/100 = $345
Thus, simple interest for 1 year = $345
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $345 × 3 = $1035
Thus, Simple Interest (SI) = $1035
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3450 + $1035
= $4485
Thus, Amount to be paid = $4485 Answer
Similar Questions
(1) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $7172 to clear the loan, then find the time period of the loan.
(2) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $7242 to clear the loan, then find the time period of the loan.
(3) If Betty paid $5100 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(4) How much loan did Jacob borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9200 to clear it?
(5) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $7548 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Robert borrowed a sum of $3100 at 7% simple interest for 3 years.
(7) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $7854 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 5% simple interest.
(9) What amount does James have to pay after 5 years if he takes a loan of $3000 at 2% simple interest?
(10) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $9028 to clear the loan, then find the time period of the loan.