Question:
Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 8% simple interest.
Correct Answer
$9632
Solution And Explanation
Solution
Given,
Principal (P) = $5600
Rate of Simple Interest (SI) = 8%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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 × 8% × 9
= $5600 ×8/100 × 9
= 5600 × 8 × 9/100
= 44800 × 9/100
= 403200/100
= $4032
Thus, Simple Interest = $4032
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 + $4032
= $9632
Thus, Amount to be paid = $9632 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) = 8%
And, Time (t) = 9 years
Thus, Amount (A)
= $5600 + ($5600 × 8% × 9)
= $5600 + ($5600 ×8/100 × 9)
= $5600 + (5600 × 8 × 9/100)
= $5600 + (44800 × 9/100)
= $5600 + (403200/100)
= $5600 + $4032 = $9632
Thus, Amount (A) to be paid = $9632 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $5600, the simple interest in 1 year
= 8/100 × 5600
= 8 × 5600/100
= 44800/100 = $448
Thus, simple interest for 1 year = $448
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $448 × 9 = $4032
Thus, Simple Interest (SI) = $4032
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5600 + $4032
= $9632
Thus, Amount to be paid = $9632 Answer
Similar Questions
(1) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 5% simple interest?
(2) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $10064 to clear the loan, then find the time period of the loan.
(3) What amount will be due after 2 years if William borrowed a sum of $3250 at a 8% simple interest?
(4) If Betty paid $4930 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(5) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $8580 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if William borrowed a sum of $3500 at 2% simple interest for 4 years.
(7) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $11900 to clear the loan, then find the time period of the loan.
(8) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $8965 to clear the loan, then find the time period of the loan.
(9) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $8820 to clear the loan, then find the time period of the loan.
(10) Michelle had to pay $5395.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.