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) How much loan did Andrew borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7820 to clear it?
(2) What amount does James have to pay after 6 years if he takes a loan of $3000 at 8% simple interest?
(3) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6300 to clear it?
(4) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $9984 to clear the loan, then find the time period of the loan.
(5) In how much time a principal of $3200 will amount to $3456 at a simple interest of 4% per annum?
(6) How much loan did Carol borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8107.5 to clear it?
(7) What amount does David have to pay after 6 years if he takes a loan of $3400 at 8% simple interest?
(8) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 5% simple interest for 3 years.
(9) How much loan did Ryan borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9875 to clear it?
(10) Calculate the amount due if Sarah borrowed a sum of $3850 at 4% simple interest for 3 years.