Question:
Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 5% simple interest.
Correct Answer
$7612.5
Solution And Explanation
Solution
Given,
Principal (P) = $5250
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) = $5250 × 5% × 9
= $5250 ×5/100 × 9
= 5250 × 5 × 9/100
= 26250 × 9/100
= 236250/100
= $2362.5
Thus, Simple Interest = $2362.5
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 = $5250 + $2362.5
= $7612.5
Thus, Amount to be paid = $7612.5 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 = $5250
Rate of Simple Interest (SI) or (R) = 5%
And, Time (t) = 9 years
Thus, Amount (A)
= $5250 + ($5250 × 5% × 9)
= $5250 + ($5250 ×5/100 × 9)
= $5250 + (5250 × 5 × 9/100)
= $5250 + (26250 × 9/100)
= $5250 + (236250/100)
= $5250 + $2362.5 = $7612.5
Thus, Amount (A) to be paid = $7612.5 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 $5250, the simple interest in 1 year
= 5/100 × 5250
= 5 × 5250/100
= 26250/100 = $262.5
Thus, simple interest for 1 year = $262.5
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $262.5 × 9 = $2362.5
Thus, Simple Interest (SI) = $2362.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5250 + $2362.5
= $7612.5
Thus, Amount to be paid = $7612.5 Answer
Similar Questions
(1) What amount will be due after 2 years if William borrowed a sum of $3250 at a 7% simple interest?
(2) 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.
(3) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 9% simple interest?
(4) How much loan did Margaret borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7937.5 to clear it?
(5) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 10% simple interest?
(6) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $10148 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 2% simple interest.
(8) If Joseph paid $4440 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(9) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $10660 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Thomas borrowed a sum of $3800 at 8% simple interest for 3 years.