Question:
Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 2% simple interest.
Correct Answer
$6313
Solution And Explanation
Solution
Given,
Principal (P) = $5350
Rate of Simple Interest (SI) = 2%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 2% simple interest means, Rate of Simple Interest (SI) is 2% 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 × 2% × 9
= $5350 ×2/100 × 9
= 5350 × 2 × 9/100
= 10700 × 9/100
= 96300/100
= $963
Thus, Simple Interest = $963
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 + $963
= $6313
Thus, Amount to be paid = $6313 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) = 2%
And, Time (t) = 9 years
Thus, Amount (A)
= $5350 + ($5350 × 2% × 9)
= $5350 + ($5350 ×2/100 × 9)
= $5350 + (5350 × 2 × 9/100)
= $5350 + (10700 × 9/100)
= $5350 + (96300/100)
= $5350 + $963 = $6313
Thus, Amount (A) to be paid = $6313 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 2%
This, means, $2 per $100 per year
∵ For $100, the simple interest for 1 year = $2
∴ For $1, the simple interest for 1 year = 2/100
∴ For $5350, the simple interest in 1 year
= 2/100 × 5350
= 2 × 5350/100
= 10700/100 = $107
Thus, simple interest for 1 year = $107
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $107 × 9 = $963
Thus, Simple Interest (SI) = $963
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5350 + $963
= $6313
Thus, Amount to be paid = $6313 Answer
Similar Questions
(1) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $10764 to clear the loan, then find the time period of the loan.
(2) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $7052 to clear the loan, then find the time period of the loan.
(3) How much loan did Richard borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6160 to clear it?
(4) How much loan did Daniel borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6710 to clear it?
(5) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 10% simple interest?
(6) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 9% simple interest for 8 years.
(7) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 5% simple interest for 8 years.
(8) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $10000 to clear the loan, then find the time period of the loan.
(9) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $10200 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 9% simple interest.