Question:
What amount does David have to pay after 6 years if he takes a loan of $3400 at 8% simple interest?
Correct Answer
$5032
Solution And Explanation
Solution
Given,
Principal (P) = $3400
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) = $3400 × 8% × 6
= $3400 ×8/100 × 6
= 3400 × 8 × 6/100
= 27200 × 6/100
= 163200/100
= $1632
Thus, Simple Interest = $1632
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 = $3400 + $1632
= $5032
Thus, Amount to be paid = $5032 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 = $3400
Rate of Simple Interest (SI) or (R) = 8%
And, Time (t) = 6 years
Thus, Amount (A)
= $3400 + ($3400 × 8% × 6)
= $3400 + ($3400 ×8/100 × 6)
= $3400 + (3400 × 8 × 6/100)
= $3400 + (27200 × 6/100)
= $3400 + (163200/100)
= $3400 + $1632 = $5032
Thus, Amount (A) to be paid = $5032 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 $3400, the simple interest in 1 year
= 8/100 × 3400
= 8 × 3400/100
= 27200/100 = $272
Thus, simple interest for 1 year = $272
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $272 × 6 = $1632
Thus, Simple Interest (SI) = $1632
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3400 + $1632
= $5032
Thus, Amount to be paid = $5032 Answer
Similar Questions
(1) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $12800 to clear the loan, then find the time period of the loan.
(2) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 5% simple interest?
(3) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $12420 to clear the loan, then find the time period of the loan.
(4) If Joseph paid $3996 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(5) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8745 to clear it?
(6) Find the amount to be paid if William borrowed a sum of $5500 at 10% simple interest for 8 years.
(7) If Thomas paid $4256 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(8) Find the amount to be paid if William borrowed a sum of $5500 at 3% simple interest for 8 years.
(9) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 9% simple interest?
(10) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $6683 to clear the loan, then find the time period of the loan.