Question:
Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 6% simple interest.
Correct Answer
$9086
Solution And Explanation
Solution
Given,
Principal (P) = $5900
Rate of Simple Interest (SI) = 6%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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) = $5900 × 6% × 9
= $5900 ×6/100 × 9
= 5900 × 6 × 9/100
= 35400 × 9/100
= 318600/100
= $3186
Thus, Simple Interest = $3186
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 = $5900 + $3186
= $9086
Thus, Amount to be paid = $9086 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 = $5900
Rate of Simple Interest (SI) or (R) = 6%
And, Time (t) = 9 years
Thus, Amount (A)
= $5900 + ($5900 × 6% × 9)
= $5900 + ($5900 ×6/100 × 9)
= $5900 + (5900 × 6 × 9/100)
= $5900 + (35400 × 9/100)
= $5900 + (318600/100)
= $5900 + $3186 = $9086
Thus, Amount (A) to be paid = $9086 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $5900, the simple interest in 1 year
= 6/100 × 5900
= 6 × 5900/100
= 35400/100 = $354
Thus, simple interest for 1 year = $354
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $354 × 9 = $3186
Thus, Simple Interest (SI) = $3186
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5900 + $3186
= $9086
Thus, Amount to be paid = $9086 Answer
Similar Questions
(1) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Joseph borrowed a sum of $5700 at 9% simple interest for 7 years.
(3) Calculate the amount due if Jessica borrowed a sum of $3750 at 5% simple interest for 4 years.
(4) How much loan did Kevin borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7810 to clear it?
(5) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $9834 to clear the loan, then find the time period of the loan.
(6) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $11730 to clear the loan, then find the time period of the loan.
(7) If Barbara paid $4118 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(8) Find the amount to be paid if Patricia borrowed a sum of $5150 at 6% simple interest for 7 years.
(9) What amount does David have to pay after 5 years if he takes a loan of $3400 at 6% simple interest?
(10) Calculate the amount due if Jessica borrowed a sum of $3750 at 2% simple interest for 3 years.