Question:
Find the amount to be paid if Susan borrowed a sum of $5650 at 8% simple interest for 7 years.
Correct Answer
$8814
Solution And Explanation
Solution
Given,
Principal (P) = $5650
Rate of Simple Interest (SI) = 8%
Time (t) = 7 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) = $5650 × 8% × 7
= $5650 ×8/100 × 7
= 5650 × 8 × 7/100
= 45200 × 7/100
= 316400/100
= $3164
Thus, Simple Interest = $3164
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 + $3164
= $8814
Thus, Amount to be paid = $8814 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) = 8%
And, Time (t) = 7 years
Thus, Amount (A)
= $5650 + ($5650 × 8% × 7)
= $5650 + ($5650 ×8/100 × 7)
= $5650 + (5650 × 8 × 7/100)
= $5650 + (45200 × 7/100)
= $5650 + (316400/100)
= $5650 + $3164 = $8814
Thus, Amount (A) to be paid = $8814 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 $5650, the simple interest in 1 year
= 8/100 × 5650
= 8 × 5650/100
= 45200/100 = $452
Thus, simple interest for 1 year = $452
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $452 × 7 = $3164
Thus, Simple Interest (SI) = $3164
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5650 + $3164
= $8814
Thus, Amount to be paid = $8814 Answer
Similar Questions
(1) In how much time a principal of $3150 will amount to $3622.5 at a simple interest of 5% per annum?
(2) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $7421 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Patricia borrowed a sum of $5150 at 7% simple interest for 8 years.
(4) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 8% simple interest.
(5) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $11584 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 3% simple interest.
(7) John had to pay $3488 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(8) Calculate the amount due if Sarah borrowed a sum of $3850 at 10% simple interest for 3 years.
(9) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 10% simple interest?
(10) If David borrowed $3400 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.