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) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 3% simple interest?
(2) If Steven paid $4968 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(3) How much loan did Mary borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5807.5 to clear it?
(4) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $8732 to clear the loan, then find the time period of the loan.
(5) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 3% simple interest?
(6) Calculate the amount due if William borrowed a sum of $3500 at 4% simple interest for 3 years.
(7) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 8% simple interest.
(8) James had to pay $3450 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(9) Calculate the amount due if Robert borrowed a sum of $3100 at 4% simple interest for 4 years.
(10) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $6800 to clear the loan, then find the time period of the loan.