Question:
Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 7% simple interest.
Correct Answer
$9095
Solution And Explanation
Solution
Given,
Principal (P) = $5350
Rate of Simple Interest (SI) = 7%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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 × 7% × 10
= $5350 ×7/100 × 10
= 5350 × 7 × 10/100
= 37450 × 10/100
= 374500/100
= $3745
Thus, Simple Interest = $3745
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 + $3745
= $9095
Thus, Amount to be paid = $9095 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) = 7%
And, Time (t) = 10 years
Thus, Amount (A)
= $5350 + ($5350 × 7% × 10)
= $5350 + ($5350 ×7/100 × 10)
= $5350 + (5350 × 7 × 10/100)
= $5350 + (37450 × 10/100)
= $5350 + (374500/100)
= $5350 + $3745 = $9095
Thus, Amount (A) to be paid = $9095 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $5350, the simple interest in 1 year
= 7/100 × 5350
= 7 × 5350/100
= 37450/100 = $374.5
Thus, simple interest for 1 year = $374.5
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $374.5 × 10 = $3745
Thus, Simple Interest (SI) = $3745
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5350 + $3745
= $9095
Thus, Amount to be paid = $9095 Answer
Similar Questions
(1) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $6528 to clear the loan, then find the time period of the loan.
(2) How much loan did George borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9125 to clear it?
(3) Find the amount to be paid if Linda borrowed a sum of $5350 at 2% simple interest for 7 years.
(4) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $9600 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 9% simple interest.
(6) If Susan paid $4380 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(7) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $10106 to clear the loan, then find the time period of the loan.
(8) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $11200 to clear the loan, then find the time period of the loan.
(9) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 4% simple interest?
(10) In how much time a principal of $3200 will amount to $3680 at a simple interest of 3% per annum?