Question:
Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 5% simple interest.
Correct Answer
$8475
Solution And Explanation
Solution
Given,
Principal (P) = $5650
Rate of Simple Interest (SI) = 5%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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) = $5650 × 5% × 10
= $5650 ×5/100 × 10
= 5650 × 5 × 10/100
= 28250 × 10/100
= 282500/100
= $2825
Thus, Simple Interest = $2825
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 = $5650 + $2825
= $8475
Thus, Amount to be paid = $8475 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 = $5650
Rate of Simple Interest (SI) or (R) = 5%
And, Time (t) = 10 years
Thus, Amount (A)
= $5650 + ($5650 × 5% × 10)
= $5650 + ($5650 ×5/100 × 10)
= $5650 + (5650 × 5 × 10/100)
= $5650 + (28250 × 10/100)
= $5650 + (282500/100)
= $5650 + $2825 = $8475
Thus, Amount (A) to be paid = $8475 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $5650, the simple interest in 1 year
= 5/100 × 5650
= 5 × 5650/100
= 28250/100 = $282.5
Thus, simple interest for 1 year = $282.5
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $282.5 × 10 = $2825
Thus, Simple Interest (SI) = $2825
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5650 + $2825
= $8475
Thus, Amount to be paid = $8475 Answer
Similar Questions
(1) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.
(2) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $10988 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Sarah borrowed a sum of $3850 at 2% simple interest for 3 years.
(4) David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $7488 to clear the loan, then find the time period of the loan.
(5) How much loan did Jacob borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9600 to clear it?
(6) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 6% simple interest?
(7) Calculate the amount due if Thomas borrowed a sum of $3800 at 3% simple interest for 4 years.
(8) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $7400 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Patricia borrowed a sum of $5150 at 6% simple interest for 8 years.
(10) If Richard paid $4320 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.