Question:
Calculate the amount due if Elizabeth borrowed a sum of $3450 at 9% simple interest for 4 years.
Correct Answer
$4692
Solution And Explanation
Solution
Given,
Principal (P) = $3450
Rate of Simple Interest (SI) = 9%
Time (t) = 4 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% 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 × 9% × 4
= $3450 ×9/100 × 4
= 3450 × 9 × 4/100
= 31050 × 4/100
= 124200/100
= $1242
Thus, Simple Interest = $1242
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 + $1242
= $4692
Thus, Amount to be paid = $4692 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) = 9%
And, Time (t) = 4 years
Thus, Amount (A)
= $3450 + ($3450 × 9% × 4)
= $3450 + ($3450 ×9/100 × 4)
= $3450 + (3450 × 9 × 4/100)
= $3450 + (31050 × 4/100)
= $3450 + (124200/100)
= $3450 + $1242 = $4692
Thus, Amount (A) to be paid = $4692 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 9%
This, means, $9 per $100 per year
∵ For $100, the simple interest for 1 year = $9
∴ For $1, the simple interest for 1 year = 9/100
∴ For $3450, the simple interest in 1 year
= 9/100 × 3450
= 9 × 3450/100
= 31050/100 = $310.5
Thus, simple interest for 1 year = $310.5
Therefore, simple interest for 4 years
= Simple interest for 1 year × 4
= $310.5 × 4 = $1242
Thus, Simple Interest (SI) = $1242
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3450 + $1242
= $4692
Thus, Amount to be paid = $4692 Answer
Similar Questions
(1) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $7104 to clear the loan, then find the time period of the loan.
(2) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $8436 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 2% simple interest.
(4) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 6% simple interest?
(5) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $8704 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Joseph borrowed a sum of $5700 at 8% simple interest for 7 years.
(7) How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8970 to clear it?
(8) Thomas had to pay $4142 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(9) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 3% simple interest?
(10) Calculate the amount due if Sarah borrowed a sum of $3850 at 5% simple interest for 3 years.