Question:
Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 5% simple interest.
Correct Answer
$7395
Solution And Explanation
Solution
Given,
Principal (P) = $5100
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) = $5100 × 5% × 9
= $5100 ×5/100 × 9
= 5100 × 5 × 9/100
= 25500 × 9/100
= 229500/100
= $2295
Thus, Simple Interest = $2295
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 = $5100 + $2295
= $7395
Thus, Amount to be paid = $7395 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 = $5100
Rate of Simple Interest (SI) or (R) = 5%
And, Time (t) = 9 years
Thus, Amount (A)
= $5100 + ($5100 × 5% × 9)
= $5100 + ($5100 ×5/100 × 9)
= $5100 + (5100 × 5 × 9/100)
= $5100 + (25500 × 9/100)
= $5100 + (229500/100)
= $5100 + $2295 = $7395
Thus, Amount (A) to be paid = $7395 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 $5100, the simple interest in 1 year
= 5/100 × 5100
= 5 × 5100/100
= 25500/100 = $255
Thus, simple interest for 1 year = $255
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $255 × 9 = $2295
Thus, Simple Interest (SI) = $2295
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5100 + $2295
= $7395
Thus, Amount to be paid = $7395 Answer
Similar Questions
(1) Calculate the amount due if John borrowed a sum of $3200 at 3% simple interest for 3 years.
(2) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 10% simple interest?
(3) If Mark paid $5104 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(4) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 3% simple interest?
(5) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 7% simple interest?
(6) How much loan did Sarah borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7020 to clear it?
(7) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $7920 to clear the loan, then find the time period of the loan.
(8) Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $8344 to clear the loan, then find the time period of the loan.
(9) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $10830 to clear the loan, then find the time period of the loan.
(10) How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9360 to clear it?