Question:
Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 4% simple interest.
Correct Answer
$7684
Solution And Explanation
Solution
Given,
Principal (P) = $5650
Rate of Simple Interest (SI) = 4%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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 × 4% × 9
= $5650 ×4/100 × 9
= 5650 × 4 × 9/100
= 22600 × 9/100
= 203400/100
= $2034
Thus, Simple Interest = $2034
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 + $2034
= $7684
Thus, Amount to be paid = $7684 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) = 4%
And, Time (t) = 9 years
Thus, Amount (A)
= $5650 + ($5650 × 4% × 9)
= $5650 + ($5650 ×4/100 × 9)
= $5650 + (5650 × 4 × 9/100)
= $5650 + (22600 × 9/100)
= $5650 + (203400/100)
= $5650 + $2034 = $7684
Thus, Amount (A) to be paid = $7684 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $5650, the simple interest in 1 year
= 4/100 × 5650
= 4 × 5650/100
= 22600/100 = $226
Thus, simple interest for 1 year = $226
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $226 × 9 = $2034
Thus, Simple Interest (SI) = $2034
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5650 + $2034
= $7684
Thus, Amount to be paid = $7684 Answer
Similar Questions
(1) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $6622 to clear the loan, then find the time period of the loan.
(2) How much loan did Patricia borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5922.5 to clear it?
(3) Find the amount to be paid if Robert borrowed a sum of $5100 at 4% simple interest for 7 years.
(4) Calculate the amount due if Robert borrowed a sum of $3100 at 9% simple interest for 3 years.
(5) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 8% simple interest?
(6) Find the amount to be paid if Jessica borrowed a sum of $5750 at 2% simple interest for 7 years.
(7) Calculate the amount due if Sarah borrowed a sum of $3850 at 9% simple interest for 4 years.
(8) Find the amount to be paid if David borrowed a sum of $5400 at 9% simple interest for 8 years.
(9) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $8493 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Mary borrowed a sum of $3050 at 7% simple interest for 3 years.