Question:
Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 5% simple interest.
Correct Answer
$8265
Solution And Explanation
Solution
Given,
Principal (P) = $5700
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) = $5700 × 5% × 9
= $5700 ×5/100 × 9
= 5700 × 5 × 9/100
= 28500 × 9/100
= 256500/100
= $2565
Thus, Simple Interest = $2565
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 = $5700 + $2565
= $8265
Thus, Amount to be paid = $8265 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 = $5700
Rate of Simple Interest (SI) or (R) = 5%
And, Time (t) = 9 years
Thus, Amount (A)
= $5700 + ($5700 × 5% × 9)
= $5700 + ($5700 ×5/100 × 9)
= $5700 + (5700 × 5 × 9/100)
= $5700 + (28500 × 9/100)
= $5700 + (256500/100)
= $5700 + $2565 = $8265
Thus, Amount (A) to be paid = $8265 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 $5700, the simple interest in 1 year
= 5/100 × 5700
= 5 × 5700/100
= 28500/100 = $285
Thus, simple interest for 1 year = $285
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $285 × 9 = $2565
Thus, Simple Interest (SI) = $2565
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5700 + $2565
= $8265
Thus, Amount to be paid = $8265 Answer
Similar Questions
(1) Find the amount to be paid if Richard borrowed a sum of $5600 at 5% simple interest for 7 years.
(2) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 4% simple interest?
(3) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 9% simple interest.
(4) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 10% simple interest?
(5) How much loan did Michael borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6625 to clear it?
(6) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 8% simple interest?
(7) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 5% simple interest?
(8) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9062.5 to clear it?
(9) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $9372 to clear the loan, then find the time period of the loan.
(10) If Sarah paid $4312 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.