Question:
Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 9% simple interest.
Correct Answer
$10735
Solution And Explanation
Solution
Given,
Principal (P) = $5650
Rate of Simple Interest (SI) = 9%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% 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 × 9% × 10
= $5650 ×9/100 × 10
= 5650 × 9 × 10/100
= 50850 × 10/100
= 508500/100
= $5085
Thus, Simple Interest = $5085
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 + $5085
= $10735
Thus, Amount to be paid = $10735 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) = 9%
And, Time (t) = 10 years
Thus, Amount (A)
= $5650 + ($5650 × 9% × 10)
= $5650 + ($5650 ×9/100 × 10)
= $5650 + (5650 × 9 × 10/100)
= $5650 + (50850 × 10/100)
= $5650 + (508500/100)
= $5650 + $5085 = $10735
Thus, Amount (A) to be paid = $10735 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 9%
This, means, $9 per $100 per year
∵ For $100, the simple interest for 1 year = $9
∴ For $1, the simple interest for 1 year = 9/100
∴ For $5650, the simple interest in 1 year
= 9/100 × 5650
= 9 × 5650/100
= 50850/100 = $508.5
Thus, simple interest for 1 year = $508.5
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $508.5 × 10 = $5085
Thus, Simple Interest (SI) = $5085
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5650 + $5085
= $10735
Thus, Amount to be paid = $10735 Answer
Similar Questions
(1) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 9% simple interest?
(2) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $5712 to clear the loan, then find the time period of the loan.
(3) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $11210 to clear the loan, then find the time period of the loan.
(4) In how much time a principal of $3050 will amount to $3538 at a simple interest of 4% per annum?
(5) Mark had to pay $4928 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(6) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 8% simple interest for 7 years.
(7) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 7% simple interest?
(8) Find the amount to be paid if Jessica borrowed a sum of $5750 at 2% simple interest for 7 years.
(9) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 7% simple interest?
(10) Find the amount to be paid if Thomas borrowed a sum of $5800 at 7% simple interest for 8 years.