Question:
What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 9% simple interest?
Correct Answer
$5313
Solution And Explanation
Solution
Given,
Principal (P) = $3450
Rate of Simple Interest (SI) = 9%
Time (t) = 6 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% × 6
= $3450 ×9/100 × 6
= 3450 × 9 × 6/100
= 31050 × 6/100
= 186300/100
= $1863
Thus, Simple Interest = $1863
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 + $1863
= $5313
Thus, Amount to be paid = $5313 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) = 6 years
Thus, Amount (A)
= $3450 + ($3450 × 9% × 6)
= $3450 + ($3450 ×9/100 × 6)
= $3450 + (3450 × 9 × 6/100)
= $3450 + (31050 × 6/100)
= $3450 + (186300/100)
= $3450 + $1863 = $5313
Thus, Amount (A) to be paid = $5313 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 6 years
= Simple interest for 1 year × 6
= $310.5 × 6 = $1863
Thus, Simple Interest (SI) = $1863
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3450 + $1863
= $5313
Thus, Amount to be paid = $5313 Answer
Similar Questions
(1) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $9984 to clear the loan, then find the time period of the loan.
(2) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 4% simple interest?
(3) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 10% simple interest?
(4) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $10132 to clear the loan, then find the time period of the loan.
(5) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $7644 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if John borrowed a sum of $3200 at 9% simple interest for 4 years.
(7) Calculate the amount due if James borrowed a sum of $3000 at 3% simple interest for 4 years.
(8) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 6% simple interest?
(9) Find the amount to be paid if Barbara borrowed a sum of $5550 at 5% simple interest for 7 years.
(10) If Karen paid $4582 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.