Question:
Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 4% simple interest.
Correct Answer
$7000
Solution And Explanation
Solution
Given,
Principal (P) = $5000
Rate of Simple Interest (SI) = 4%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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) = $5000 × 4% × 10
= $5000 ×4/100 × 10
= 5000 × 4 × 10/100
= 20000 × 10/100
= 200000/100
= $2000
Thus, Simple Interest = $2000
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 = $5000 + $2000
= $7000
Thus, Amount to be paid = $7000 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 = $5000
Rate of Simple Interest (SI) or (R) = 4%
And, Time (t) = 10 years
Thus, Amount (A)
= $5000 + ($5000 × 4% × 10)
= $5000 + ($5000 ×4/100 × 10)
= $5000 + (5000 × 4 × 10/100)
= $5000 + (20000 × 10/100)
= $5000 + (200000/100)
= $5000 + $2000 = $7000
Thus, Amount (A) to be paid = $7000 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $5000, the simple interest in 1 year
= 4/100 × 5000
= 4 × 5000/100
= 20000/100 = $200
Thus, simple interest for 1 year = $200
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $200 × 10 = $2000
Thus, Simple Interest (SI) = $2000
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5000 + $2000
= $7000
Thus, Amount to be paid = $7000 Answer
Similar Questions
(1) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $9350 to clear the loan, then find the time period of the loan.
(2) In how much time a principal of $3000 will amount to $3480 at a simple interest of 4% per annum?
(3) How much loan did James borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5750 to clear it?
(4) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 8% simple interest?
(5) In how much time a principal of $3200 will amount to $3712 at a simple interest of 4% per annum?
(6) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $8550 to clear the loan, then find the time period of the loan.
(7) How much loan did Charles borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7375 to clear it?
(8) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $9288 to clear the loan, then find the time period of the loan.
(9) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 9% simple interest?
(10) Find the amount to be paid if Barbara borrowed a sum of $5550 at 3% simple interest for 8 years.