Question:
Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 5% simple interest.
Correct Answer
$8120
Solution And Explanation
Solution
Given,
Principal (P) = $5600
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) = $5600 × 5% × 9
= $5600 ×5/100 × 9
= 5600 × 5 × 9/100
= 28000 × 9/100
= 252000/100
= $2520
Thus, Simple Interest = $2520
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 = $5600 + $2520
= $8120
Thus, Amount to be paid = $8120 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 = $5600
Rate of Simple Interest (SI) or (R) = 5%
And, Time (t) = 9 years
Thus, Amount (A)
= $5600 + ($5600 × 5% × 9)
= $5600 + ($5600 ×5/100 × 9)
= $5600 + (5600 × 5 × 9/100)
= $5600 + (28000 × 9/100)
= $5600 + (252000/100)
= $5600 + $2520 = $8120
Thus, Amount (A) to be paid = $8120 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 $5600, the simple interest in 1 year
= 5/100 × 5600
= 5 × 5600/100
= 28000/100 = $280
Thus, simple interest for 1 year = $280
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $280 × 9 = $2520
Thus, Simple Interest (SI) = $2520
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5600 + $2520
= $8120
Thus, Amount to be paid = $8120 Answer
Similar Questions
(1) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $13000 to clear the loan, then find the time period of the loan.
(2) Matthew had to pay $4578 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(3) Calculate the amount due if Sarah borrowed a sum of $3850 at 9% simple interest for 4 years.
(4) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 8% simple interest?
(5) If Anthony paid $4644 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(6) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $8330 to clear the loan, then find the time period of the loan.
(7) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 7% simple interest?
(8) If Nancy paid $4482 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(9) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $6956 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 8% simple interest.