Question:
What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 7% simple interest?
Correct Answer
$4899
Solution And Explanation
Solution
Given,
Principal (P) = $3450
Rate of Simple Interest (SI) = 7%
Time (t) = 6 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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 × 7% × 6
= $3450 ×7/100 × 6
= 3450 × 7 × 6/100
= 24150 × 6/100
= 144900/100
= $1449
Thus, Simple Interest = $1449
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 + $1449
= $4899
Thus, Amount to be paid = $4899 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) = 7%
And, Time (t) = 6 years
Thus, Amount (A)
= $3450 + ($3450 × 7% × 6)
= $3450 + ($3450 ×7/100 × 6)
= $3450 + (3450 × 7 × 6/100)
= $3450 + (24150 × 6/100)
= $3450 + (144900/100)
= $3450 + $1449 = $4899
Thus, Amount (A) to be paid = $4899 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $3450, the simple interest in 1 year
= 7/100 × 3450
= 7 × 3450/100
= 24150/100 = $241.5
Thus, simple interest for 1 year = $241.5
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $241.5 × 6 = $1449
Thus, Simple Interest (SI) = $1449
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3450 + $1449
= $4899
Thus, Amount to be paid = $4899 Answer
Similar Questions
(1) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 9% simple interest?
(2) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $10679 to clear the loan, then find the time period of the loan.
(3) Barbara had to pay $3763 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(4) Find the amount to be paid if Robert borrowed a sum of $5100 at 10% simple interest for 7 years.
(5) Betty had to pay $4505 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(6) Find the amount to be paid if Linda borrowed a sum of $5350 at 4% simple interest for 7 years.
(7) Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $5964 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Patricia borrowed a sum of $3150 at 9% simple interest for 4 years.
(9) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 2% simple interest.
(10) Calculate the amount due if William borrowed a sum of $3500 at 9% simple interest for 3 years.