Question:
Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 8% simple interest.
Correct Answer
$8944
Solution And Explanation
Solution
Given,
Principal (P) = $5200
Rate of Simple Interest (SI) = 8%
Time (t) = 9 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) = $5200 × 8% × 9
= $5200 ×8/100 × 9
= 5200 × 8 × 9/100
= 41600 × 9/100
= 374400/100
= $3744
Thus, Simple Interest = $3744
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 = $5200 + $3744
= $8944
Thus, Amount to be paid = $8944 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 = $5200
Rate of Simple Interest (SI) or (R) = 8%
And, Time (t) = 9 years
Thus, Amount (A)
= $5200 + ($5200 × 8% × 9)
= $5200 + ($5200 ×8/100 × 9)
= $5200 + (5200 × 8 × 9/100)
= $5200 + (41600 × 9/100)
= $5200 + (374400/100)
= $5200 + $3744 = $8944
Thus, Amount (A) to be paid = $8944 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 $5200, the simple interest in 1 year
= 8/100 × 5200
= 8 × 5200/100
= 41600/100 = $416
Thus, simple interest for 1 year = $416
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $416 × 9 = $3744
Thus, Simple Interest (SI) = $3744
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5200 + $3744
= $8944
Thus, Amount to be paid = $8944 Answer
Similar Questions
(1) Calculate the amount due if Susan borrowed a sum of $3650 at 10% simple interest for 3 years.
(2) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $8280 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Robert borrowed a sum of $5100 at 3% simple interest for 7 years.
(4) How much loan did Susan borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7062.5 to clear it?
(5) Find the amount to be paid if Joseph borrowed a sum of $5700 at 4% simple interest for 8 years.
(6) Find the amount to be paid if Charles borrowed a sum of $5900 at 3% simple interest for 8 years.
(7) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6683 to clear the loan, then find the time period of the loan.
(8) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $6106 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 4% simple interest.
(10) If Daniel paid $4920 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.