Question:
Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 5% simple interest.
Correct Answer
$8555
Solution And Explanation
Solution
Given,
Principal (P) = $5900
Rate of Simple Interest (SI) = 5%
Time (t) = 9 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) = $5900 × 5% × 9
= $5900 ×5/100 × 9
= 5900 × 5 × 9/100
= 29500 × 9/100
= 265500/100
= $2655
Thus, Simple Interest = $2655
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 + $2655
= $8555
Thus, Amount to be paid = $8555 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) = 5%
And, Time (t) = 9 years
Thus, Amount (A)
= $5900 + ($5900 × 5% × 9)
= $5900 + ($5900 ×5/100 × 9)
= $5900 + (5900 × 5 × 9/100)
= $5900 + (29500 × 9/100)
= $5900 + (265500/100)
= $5900 + $2655 = $8555
Thus, Amount (A) to be paid = $8555 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 $5900, the simple interest in 1 year
= 5/100 × 5900
= 5 × 5900/100
= 29500/100 = $295
Thus, simple interest for 1 year = $295
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $295 × 9 = $2655
Thus, Simple Interest (SI) = $2655
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5900 + $2655
= $8555
Thus, Amount to be paid = $8555 Answer
Similar Questions
(1) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $10140 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 2% simple interest.
(3) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $7009 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Barbara borrowed a sum of $5550 at 5% simple interest for 7 years.
(5) Calculate the amount due if Michael borrowed a sum of $3300 at 3% simple interest for 3 years.
(6) Nancy had to pay $4648 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(7) If Andrew paid $5568 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(8) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 2% simple interest?
(9) Donald had to pay $5040 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(10) What amount does James have to pay after 6 years if he takes a loan of $3000 at 6% simple interest?