Question:
Find the amount to be paid if John borrowed a sum of $5200 at 4% simple interest for 8 years.
Correct Answer
$6864
Solution And Explanation
Solution
Given,
Principal (P) = $5200
Rate of Simple Interest (SI) = 4%
Time (t) = 8 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) = $5200 × 4% × 8
= $5200 ×4/100 × 8
= 5200 × 4 × 8/100
= 20800 × 8/100
= 166400/100
= $1664
Thus, Simple Interest = $1664
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 = $5200 + $1664
= $6864
Thus, Amount to be paid = $6864 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 = $5200
Rate of Simple Interest (SI) or (R) = 4%
And, Time (t) = 8 years
Thus, Amount (A)
= $5200 + ($5200 × 4% × 8)
= $5200 + ($5200 ×4/100 × 8)
= $5200 + (5200 × 4 × 8/100)
= $5200 + (20800 × 8/100)
= $5200 + (166400/100)
= $5200 + $1664 = $6864
Thus, Amount (A) to be paid = $6864 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 $5200, the simple interest in 1 year
= 4/100 × 5200
= 4 × 5200/100
= 20800/100 = $208
Thus, simple interest for 1 year = $208
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $208 × 8 = $1664
Thus, Simple Interest (SI) = $1664
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5200 + $1664
= $6864
Thus, Amount to be paid = $6864 Answer
Similar Questions
(1) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $12350 to clear the loan, then find the time period of the loan.
(2) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 6% simple interest?
(3) Steven had to pay $4876 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(4) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $10780 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Karen borrowed a sum of $5950 at 6% simple interest for 8 years.
(6) How much loan did Joseph borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7125 to clear it?
(7) How much loan did Amanda borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8937.5 to clear it?
(8) Find the amount to be paid if Linda borrowed a sum of $5350 at 2% simple interest for 7 years.
(9) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $8624 to clear the loan, then find the time period of the loan.
(10) If Charles paid $4524 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.