Question:
Find the amount to be paid if Susan borrowed a sum of $5650 at 10% simple interest for 8 years.
Correct Answer
$10170
Solution And Explanation
Solution
Given,
Principal (P) = $5650
Rate of Simple Interest (SI) = 10%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 8
= $5650 ×10/100 × 8
= 5650 × 10 × 8/100
= 56500 × 8/100
= 452000/100
= $4520
Thus, Simple Interest = $4520
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 + $4520
= $10170
Thus, Amount to be paid = $10170 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) = 10%
And, Time (t) = 8 years
Thus, Amount (A)
= $5650 + ($5650 × 10% × 8)
= $5650 + ($5650 ×10/100 × 8)
= $5650 + (5650 × 10 × 8/100)
= $5650 + (56500 × 8/100)
= $5650 + (452000/100)
= $5650 + $4520 = $10170
Thus, Amount (A) to be paid = $10170 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $5650, the simple interest in 1 year
= 10/100 × 5650
= 10 × 5650/100
= 56500/100 = $565
Thus, simple interest for 1 year = $565
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $565 × 8 = $4520
Thus, Simple Interest (SI) = $4520
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5650 + $4520
= $10170
Thus, Amount to be paid = $10170 Answer
Similar Questions
(1) If Daniel paid $4756 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(2) Find the amount to be paid if Jessica borrowed a sum of $5750 at 4% simple interest for 7 years.
(3) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $9116 to clear the loan, then find the time period of the loan.
(4) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $8316 to clear the loan, then find the time period of the loan.
(5) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $10492 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Robert borrowed a sum of $5100 at 10% simple interest for 8 years.
(7) Find the amount to be paid if Jessica borrowed a sum of $5750 at 5% simple interest for 7 years.
(8) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $5822 to clear the loan, then find the time period of the loan.
(9) In how much time a principal of $3000 will amount to $3450 at a simple interest of 5% per annum?
(10) In how much time a principal of $3000 will amount to $3240 at a simple interest of 2% per annum?