Question:
Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 6% simple interest.
Correct Answer
$8932
Solution And Explanation
Solution
Given,
Principal (P) = $5800
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) = $5800 × 6% × 9
= $5800 ×6/100 × 9
= 5800 × 6 × 9/100
= 34800 × 9/100
= 313200/100
= $3132
Thus, Simple Interest = $3132
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 = $5800 + $3132
= $8932
Thus, Amount to be paid = $8932 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 = $5800
Rate of Simple Interest (SI) or (R) = 6%
And, Time (t) = 9 years
Thus, Amount (A)
= $5800 + ($5800 × 6% × 9)
= $5800 + ($5800 ×6/100 × 9)
= $5800 + (5800 × 6 × 9/100)
= $5800 + (34800 × 9/100)
= $5800 + (313200/100)
= $5800 + $3132 = $8932
Thus, Amount (A) to be paid = $8932 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 $5800, the simple interest in 1 year
= 6/100 × 5800
= 6 × 5800/100
= 34800/100 = $348
Thus, simple interest for 1 year = $348
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $348 × 9 = $3132
Thus, Simple Interest (SI) = $3132
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5800 + $3132
= $8932
Thus, Amount to be paid = $8932 Answer
Similar Questions
(1) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $10400 to clear the loan, then find the time period of the loan.
(2) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $8428 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if James borrowed a sum of $3000 at 9% simple interest for 4 years.
(4) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $11352 to clear the loan, then find the time period of the loan.
(5) If Nancy paid $4814 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(6) In how much time a principal of $3000 will amount to $3240 at a simple interest of 2% per annum?
(7) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 9% simple interest.
(8) Andrew had to pay $5088 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(9) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 5% simple interest?
(10) What amount will be due after 2 years if James borrowed a sum of $3000 at a 10% simple interest?