Question:
Find the amount to be paid if Linda borrowed a sum of $5350 at 3% simple interest for 8 years.
Correct Answer
$6634
Solution And Explanation
Solution
Given,
Principal (P) = $5350
Rate of Simple Interest (SI) = 3%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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) = $5350 × 3% × 8
= $5350 ×3/100 × 8
= 5350 × 3 × 8/100
= 16050 × 8/100
= 128400/100
= $1284
Thus, Simple Interest = $1284
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 = $5350 + $1284
= $6634
Thus, Amount to be paid = $6634 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 = $5350
Rate of Simple Interest (SI) or (R) = 3%
And, Time (t) = 8 years
Thus, Amount (A)
= $5350 + ($5350 × 3% × 8)
= $5350 + ($5350 ×3/100 × 8)
= $5350 + (5350 × 3 × 8/100)
= $5350 + (16050 × 8/100)
= $5350 + (128400/100)
= $5350 + $1284 = $6634
Thus, Amount (A) to be paid = $6634 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $5350, the simple interest in 1 year
= 3/100 × 5350
= 3 × 5350/100
= 16050/100 = $160.5
Thus, simple interest for 1 year = $160.5
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $160.5 × 8 = $1284
Thus, Simple Interest (SI) = $1284
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5350 + $1284
= $6634
Thus, Amount to be paid = $6634 Answer
Similar Questions
(1) If Elizabeth paid $3726 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(2) Find the amount to be paid if Barbara borrowed a sum of $5550 at 6% simple interest for 8 years.
(3) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $11700 to clear the loan, then find the time period of the loan.
(4) What amount does David have to pay after 5 years if he takes a loan of $3400 at 7% simple interest?
(5) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $11200 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Sarah borrowed a sum of $3850 at 10% simple interest for 3 years.
(7) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $6930 to clear the loan, then find the time period of the loan.
(8) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $9916 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 7% simple interest.
(10) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $9128 to clear the loan, then find the time period of the loan.