Question:
Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 9% simple interest.
Correct Answer
$10545
Solution And Explanation
Solution
Given,
Principal (P) = $5550
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) = $5550 × 9% × 10
= $5550 ×9/100 × 10
= 5550 × 9 × 10/100
= 49950 × 10/100
= 499500/100
= $4995
Thus, Simple Interest = $4995
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 = $5550 + $4995
= $10545
Thus, Amount to be paid = $10545 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 = $5550
Rate of Simple Interest (SI) or (R) = 9%
And, Time (t) = 10 years
Thus, Amount (A)
= $5550 + ($5550 × 9% × 10)
= $5550 + ($5550 ×9/100 × 10)
= $5550 + (5550 × 9 × 10/100)
= $5550 + (49950 × 10/100)
= $5550 + (499500/100)
= $5550 + $4995 = $10545
Thus, Amount (A) to be paid = $10545 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 $5550, the simple interest in 1 year
= 9/100 × 5550
= 9 × 5550/100
= 49950/100 = $499.5
Thus, simple interest for 1 year = $499.5
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $499.5 × 10 = $4995
Thus, Simple Interest (SI) = $4995
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5550 + $4995
= $10545
Thus, Amount to be paid = $10545 Answer
Similar Questions
(1) Emily had to pay $5177.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(2) If Jennifer paid $3640 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(3) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $7335 to clear the loan, then find the time period of the loan.
(4) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $8840 to clear the loan, then find the time period of the loan.
(5) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $6520 to clear the loan, then find the time period of the loan.
(6) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 6% simple interest?
(7) Kenneth had to pay $5600 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(8) Find the amount to be paid if Christopher borrowed a sum of $6000 at 4% simple interest for 8 years.
(9) If Christopher borrowed $4000 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(10) Calculate the amount due if John borrowed a sum of $3200 at 5% simple interest for 3 years.