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) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $11590 to clear the loan, then find the time period of the loan.
(2) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $10664 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 8% simple interest.
(4) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $11220 to clear the loan, then find the time period of the loan.
(5) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 9% simple interest?
(6) Find the amount to be paid if Karen borrowed a sum of $5950 at 4% simple interest for 7 years.
(7) How much loan did Matthew borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6820 to clear it?
(8) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 6% simple interest?
(9) If Sarah paid $4312 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(10) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $6660 to clear the loan, then find the time period of the loan.