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) Calculate the amount due if Christopher borrowed a sum of $4000 at 5% simple interest for 3 years.
(2) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $8500 to clear the loan, then find the time period of the loan.
(3) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $6930 to clear the loan, then find the time period of the loan.
(4) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 5% simple interest?
(5) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 5% simple interest?
(6) 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.
(7) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 8% simple interest.
(8) What amount will be due after 2 years if John borrowed a sum of $3100 at a 7% simple interest?
(9) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 8% simple interest.
(10) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 5% simple interest.