Question:
Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 5% simple interest.
Correct Answer
$7757.5
Solution And Explanation
Solution
Given,
Principal (P) = $5350
Rate of Simple Interest (SI) = 5%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 9
= $5350 ×5/100 × 9
= 5350 × 5 × 9/100
= 26750 × 9/100
= 240750/100
= $2407.5
Thus, Simple Interest = $2407.5
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 + $2407.5
= $7757.5
Thus, Amount to be paid = $7757.5 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) = 5%
And, Time (t) = 9 years
Thus, Amount (A)
= $5350 + ($5350 × 5% × 9)
= $5350 + ($5350 ×5/100 × 9)
= $5350 + (5350 × 5 × 9/100)
= $5350 + (26750 × 9/100)
= $5350 + (240750/100)
= $5350 + $2407.5 = $7757.5
Thus, Amount (A) to be paid = $7757.5 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $5350, the simple interest in 1 year
= 5/100 × 5350
= 5 × 5350/100
= 26750/100 = $267.5
Thus, simple interest for 1 year = $267.5
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $267.5 × 9 = $2407.5
Thus, Simple Interest (SI) = $2407.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5350 + $2407.5
= $7757.5
Thus, Amount to be paid = $7757.5 Answer
Similar Questions
(1) Calculate the amount due if Jennifer borrowed a sum of $3250 at 5% simple interest for 3 years.
(2) If Michelle paid $5346 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(3) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 9% simple interest?
(4) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 7% simple interest?
(5) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $7844 to clear the loan, then find the time period of the loan.
(6) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $9672 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Susan borrowed a sum of $3650 at 8% simple interest for 4 years.
(8) Find the amount to be paid if William borrowed a sum of $5500 at 2% simple interest for 8 years.
(9) If Joseph paid $4144 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(10) Find the amount to be paid if Richard borrowed a sum of $5600 at 5% simple interest for 7 years.