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) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $11160 to clear the loan, then find the time period of the loan.
(2) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $8024 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 5% simple interest.
(4) Find the amount to be paid if Barbara borrowed a sum of $5550 at 2% simple interest for 8 years.
(5) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $6468 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 8% simple interest.
(7) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $7020 to clear the loan, then find the time period of the loan.
(8) In how much time a principal of $3200 will amount to $3520 at a simple interest of 5% per annum?
(9) Calculate the amount due if Linda borrowed a sum of $3350 at 6% simple interest for 4 years.
(10) How much loan did David borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5940 to clear it?