Question:
Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 10% simple interest.
Correct Answer
$10165
Solution And Explanation
Solution
Given,
Principal (P) = $5350
Rate of Simple Interest (SI) = 10%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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) = $5350 × 10% × 9
= $5350 ×10/100 × 9
= 5350 × 10 × 9/100
= 53500 × 9/100
= 481500/100
= $4815
Thus, Simple Interest = $4815
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 = $5350 + $4815
= $10165
Thus, Amount to be paid = $10165 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 = $5350
Rate of Simple Interest (SI) or (R) = 10%
And, Time (t) = 9 years
Thus, Amount (A)
= $5350 + ($5350 × 10% × 9)
= $5350 + ($5350 ×10/100 × 9)
= $5350 + (5350 × 10 × 9/100)
= $5350 + (53500 × 9/100)
= $5350 + (481500/100)
= $5350 + $4815 = $10165
Thus, Amount (A) to be paid = $10165 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $5350, the simple interest in 1 year
= 10/100 × 5350
= 10 × 5350/100
= 53500/100 = $535
Thus, simple interest for 1 year = $535
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $535 × 9 = $4815
Thus, Simple Interest (SI) = $4815
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5350 + $4815
= $10165
Thus, Amount to be paid = $10165 Answer
Similar Questions
(1) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $7854 to clear the loan, then find the time period of the loan.
(2) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $11050 to clear the loan, then find the time period of the loan.
(3) Andrew had to pay $5376 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(4) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $9230 to clear the loan, then find the time period of the loan.
(5) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 8% simple interest?
(6) 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.
(7) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.
(8) In how much time a principal of $3150 will amount to $3465 at a simple interest of 2% per annum?
(9) Calculate the amount due if Sarah borrowed a sum of $3850 at 4% simple interest for 3 years.
(10) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $9702 to clear the loan, then find the time period of the loan.