Question:
What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 8% simple interest?
Correct Answer
$5460
Solution And Explanation
Solution
Given,
Principal (P) = $3900
Rate of Simple Interest (SI) = 8%
Time (t) = 5 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% × 5
= $3900 ×8/100 × 5
= 3900 × 8 × 5/100
= 31200 × 5/100
= 156000/100
= $1560
Thus, Simple Interest = $1560
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 + $1560
= $5460
Thus, Amount to be paid = $5460 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) = 5 years
Thus, Amount (A)
= $3900 + ($3900 × 8% × 5)
= $3900 + ($3900 ×8/100 × 5)
= $3900 + (3900 × 8 × 5/100)
= $3900 + (31200 × 5/100)
= $3900 + (156000/100)
= $3900 + $1560 = $5460
Thus, Amount (A) to be paid = $5460 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 5 years
= Simple interest for 1 year × 5
= $312 × 5 = $1560
Thus, Simple Interest (SI) = $1560
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3900 + $1560
= $5460
Thus, Amount to be paid = $5460 Answer
Similar Questions
(1) Find the amount to be paid if David borrowed a sum of $5400 at 2% simple interest for 7 years.
(2) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5775 to clear it?
(3) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 10% simple interest.
(4) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $9291 to clear the loan, then find the time period of the loan.
(5) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $6705 to clear the loan, then find the time period of the loan.
(6) How much loan did Steven borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8250 to clear it?
(7) Find the amount to be paid if Robert borrowed a sum of $5100 at 7% simple interest for 8 years.
(8) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 2% simple interest for 3 years.
(9) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $7790 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if John borrowed a sum of $5200 at 5% simple interest for 7 years.