Question:
What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 8% simple interest?
Correct Answer
$5106
Solution And Explanation
Solution
Given,
Principal (P) = $3450
Rate of Simple Interest (SI) = 8%
Time (t) = 6 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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 × 8% × 6
= $3450 ×8/100 × 6
= 3450 × 8 × 6/100
= 27600 × 6/100
= 165600/100
= $1656
Thus, Simple Interest = $1656
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 + $1656
= $5106
Thus, Amount to be paid = $5106 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) = 8%
And, Time (t) = 6 years
Thus, Amount (A)
= $3450 + ($3450 × 8% × 6)
= $3450 + ($3450 ×8/100 × 6)
= $3450 + (3450 × 8 × 6/100)
= $3450 + (27600 × 6/100)
= $3450 + (165600/100)
= $3450 + $1656 = $5106
Thus, Amount (A) to be paid = $5106 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $3450, the simple interest in 1 year
= 8/100 × 3450
= 8 × 3450/100
= 27600/100 = $276
Thus, simple interest for 1 year = $276
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $276 × 6 = $1656
Thus, Simple Interest (SI) = $1656
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3450 + $1656
= $5106
Thus, Amount to be paid = $5106 Answer
Similar Questions
(1) In how much time a principal of $3200 will amount to $4000 at a simple interest of 5% per annum?
(2) Find the amount to be paid if Sarah borrowed a sum of $5850 at 9% simple interest for 7 years.
(3) Find the amount to be paid if Thomas borrowed a sum of $5800 at 6% simple interest for 8 years.
(4) Matthew had to pay $4452 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(5) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 9% simple interest?
(6) In how much time a principal of $3050 will amount to $3294 at a simple interest of 2% per annum?
(7) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $12489 to clear the loan, then find the time period of the loan.
(8) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $7980 to clear the loan, then find the time period of the loan.
(9) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $8772 to clear the loan, then find the time period of the loan.
(10) What amount will be due after 2 years if John borrowed a sum of $3100 at a 7% simple interest?