Question:
Find the amount to be paid if Susan borrowed a sum of $5650 at 5% simple interest for 8 years.
Correct Answer
$7910
Solution And Explanation
Solution
Given,
Principal (P) = $5650
Rate of Simple Interest (SI) = 5%
Time (t) = 8 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% × 8
= $5650 ×5/100 × 8
= 5650 × 5 × 8/100
= 28250 × 8/100
= 226000/100
= $2260
Thus, Simple Interest = $2260
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 + $2260
= $7910
Thus, Amount to be paid = $7910 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) = 8 years
Thus, Amount (A)
= $5650 + ($5650 × 5% × 8)
= $5650 + ($5650 ×5/100 × 8)
= $5650 + (5650 × 5 × 8/100)
= $5650 + (28250 × 8/100)
= $5650 + (226000/100)
= $5650 + $2260 = $7910
Thus, Amount (A) to be paid = $7910 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 8 years
= Simple interest for 1 year × 8
= $282.5 × 8 = $2260
Thus, Simple Interest (SI) = $2260
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5650 + $2260
= $7910
Thus, Amount to be paid = $7910 Answer
Similar Questions
(1) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 9% simple interest.
(2) What amount does David have to pay after 5 years if he takes a loan of $3400 at 6% simple interest?
(3) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 6% simple interest.
(4) Calculate the amount due if Patricia borrowed a sum of $3150 at 8% simple interest for 4 years.
(5) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $8436 to clear the loan, then find the time period of the loan.
(6) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $8140 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 8% simple interest.
(8) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 4% simple interest.
(9) If Lisa paid $4536 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(10) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 4% simple interest for 7 years.