Question:
Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 8% simple interest.
Correct Answer
$9718
Solution And Explanation
Solution
Given,
Principal (P) = $5650
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) = $5650 × 8% × 9
= $5650 ×8/100 × 9
= 5650 × 8 × 9/100
= 45200 × 9/100
= 406800/100
= $4068
Thus, Simple Interest = $4068
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 = $5650 + $4068
= $9718
Thus, Amount to be paid = $9718 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 = $5650
Rate of Simple Interest (SI) or (R) = 8%
And, Time (t) = 9 years
Thus, Amount (A)
= $5650 + ($5650 × 8% × 9)
= $5650 + ($5650 ×8/100 × 9)
= $5650 + (5650 × 8 × 9/100)
= $5650 + (45200 × 9/100)
= $5650 + (406800/100)
= $5650 + $4068 = $9718
Thus, Amount (A) to be paid = $9718 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 $5650, the simple interest in 1 year
= 8/100 × 5650
= 8 × 5650/100
= 45200/100 = $452
Thus, simple interest for 1 year = $452
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $452 × 9 = $4068
Thus, Simple Interest (SI) = $4068
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5650 + $4068
= $9718
Thus, Amount to be paid = $9718 Answer
Similar Questions
(1) Find the amount to be paid if Charles borrowed a sum of $5900 at 3% simple interest for 8 years.
(2) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Charles borrowed a sum of $5900 at 8% simple interest for 8 years.
(4) If Robert paid $3348 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(5) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 5% simple interest?
(6) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $14000 to clear the loan, then find the time period of the loan.
(7) How much loan did William borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6050 to clear it?
(8) Find the amount to be paid if Susan borrowed a sum of $5650 at 10% simple interest for 7 years.
(9) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 9% simple interest.
(10) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 7% simple interest.