Question:
What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 8% simple interest?
Correct Answer
$5772
Solution And Explanation
Solution
Given,
Principal (P) = $3900
Rate of Simple Interest (SI) = 8%
Time (t) = 6 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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) = $3900 × 8% × 6
= $3900 ×8/100 × 6
= 3900 × 8 × 6/100
= 31200 × 6/100
= 187200/100
= $1872
Thus, Simple Interest = $1872
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 = $3900 + $1872
= $5772
Thus, Amount to be paid = $5772 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 = $3900
Rate of Simple Interest (SI) or (R) = 8%
And, Time (t) = 6 years
Thus, Amount (A)
= $3900 + ($3900 × 8% × 6)
= $3900 + ($3900 ×8/100 × 6)
= $3900 + (3900 × 8 × 6/100)
= $3900 + (31200 × 6/100)
= $3900 + (187200/100)
= $3900 + $1872 = $5772
Thus, Amount (A) to be paid = $5772 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $3900, the simple interest in 1 year
= 8/100 × 3900
= 8 × 3900/100
= 31200/100 = $312
Thus, simple interest for 1 year = $312
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $312 × 6 = $1872
Thus, Simple Interest (SI) = $1872
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3900 + $1872
= $5772
Thus, Amount to be paid = $5772 Answer
Similar Questions
(1) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $9000 to clear the loan, then find the time period of the loan.
(2) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 2% simple interest?
(3) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $7052 to clear the loan, then find the time period of the loan.
(4) How much loan did Edward borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8740 to clear it?
(5) Find the amount to be paid if Christopher borrowed a sum of $6000 at 4% simple interest for 8 years.
(6) In how much time a principal of $3000 will amount to $3360 at a simple interest of 3% per annum?
(7) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 4% simple interest.
(8) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 7% simple interest?
(9) How much loan did Karen borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6842.5 to clear it?
(10) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 6% simple interest.