Question:
Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 4% simple interest.
Correct Answer
$7072
Solution And Explanation
Solution
Given,
Principal (P) = $5200
Rate of Simple Interest (SI) = 4%
Time (t) = 9 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% × 9
= $5200 ×4/100 × 9
= 5200 × 4 × 9/100
= 20800 × 9/100
= 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 = $5200 + $1872
= $7072
Thus, Amount to be paid = $7072 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) = 9 years
Thus, Amount (A)
= $5200 + ($5200 × 4% × 9)
= $5200 + ($5200 ×4/100 × 9)
= $5200 + (5200 × 4 × 9/100)
= $5200 + (20800 × 9/100)
= $5200 + (187200/100)
= $5200 + $1872 = $7072
Thus, Amount (A) to be paid = $7072 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 9 years
= Simple interest for 1 year × 9
= $208 × 9 = $1872
Thus, Simple Interest (SI) = $1872
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5200 + $1872
= $7072
Thus, Amount to be paid = $7072 Answer
Similar Questions
(1) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $6512 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Christopher borrowed a sum of $6000 at 8% simple interest for 8 years.
(3) Find the amount to be paid if Susan borrowed a sum of $5650 at 3% simple interest for 7 years.
(4) Elizabeth had to pay $3657 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(5) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 10% simple interest.
(6) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 8% simple interest?
(7) What amount does John have to pay after 5 years if he takes a loan of $3200 at 5% simple interest?
(8) How much loan did Daniel borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7015 to clear it?
(9) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $8662 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Mary borrowed a sum of $3050 at 4% simple interest for 3 years.