Question:
Find the amount to be paid if John borrowed a sum of $5200 at 5% simple interest for 8 years.
Correct Answer
$7280
Solution And Explanation
Solution
Given,
Principal (P) = $5200
Rate of Simple Interest (SI) = 5%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 8
= $5200 ×5/100 × 8
= 5200 × 5 × 8/100
= 26000 × 8/100
= 208000/100
= $2080
Thus, Simple Interest = $2080
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 + $2080
= $7280
Thus, Amount to be paid = $7280 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) = 5%
And, Time (t) = 8 years
Thus, Amount (A)
= $5200 + ($5200 × 5% × 8)
= $5200 + ($5200 ×5/100 × 8)
= $5200 + (5200 × 5 × 8/100)
= $5200 + (26000 × 8/100)
= $5200 + (208000/100)
= $5200 + $2080 = $7280
Thus, Amount (A) to be paid = $7280 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $5200, the simple interest in 1 year
= 5/100 × 5200
= 5 × 5200/100
= 26000/100 = $260
Thus, simple interest for 1 year = $260
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $260 × 8 = $2080
Thus, Simple Interest (SI) = $2080
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5200 + $2080
= $7280
Thus, Amount to be paid = $7280 Answer
Similar Questions
(1) Donald had to pay $5040 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(2) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 5% simple interest?
(3) In how much time a principal of $3150 will amount to $3654 at a simple interest of 4% per annum?
(4) In how much time a principal of $3100 will amount to $3472 at a simple interest of 4% per annum?
(5) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 3% simple interest for 8 years.
(6) How much loan did Anthony borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7560 to clear it?
(7) Find the amount to be paid if Linda borrowed a sum of $5350 at 8% simple interest for 8 years.
(8) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $8364 to clear the loan, then find the time period of the loan.
(9) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 8% simple interest?
(10) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $11730 to clear the loan, then find the time period of the loan.