Question:
Find the amount to be paid if Richard borrowed a sum of $5600 at 5% simple interest for 8 years.
Correct Answer
$7840
Solution And Explanation
Solution
Given,
Principal (P) = $5600
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) = $5600 × 5% × 8
= $5600 ×5/100 × 8
= 5600 × 5 × 8/100
= 28000 × 8/100
= 224000/100
= $2240
Thus, Simple Interest = $2240
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 = $5600 + $2240
= $7840
Thus, Amount to be paid = $7840 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 = $5600
Rate of Simple Interest (SI) or (R) = 5%
And, Time (t) = 8 years
Thus, Amount (A)
= $5600 + ($5600 × 5% × 8)
= $5600 + ($5600 ×5/100 × 8)
= $5600 + (5600 × 5 × 8/100)
= $5600 + (28000 × 8/100)
= $5600 + (224000/100)
= $5600 + $2240 = $7840
Thus, Amount (A) to be paid = $7840 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 $5600, the simple interest in 1 year
= 5/100 × 5600
= 5 × 5600/100
= 28000/100 = $280
Thus, simple interest for 1 year = $280
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $280 × 8 = $2240
Thus, Simple Interest (SI) = $2240
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5600 + $2240
= $7840
Thus, Amount to be paid = $7840 Answer
Similar Questions
(1) In how much time a principal of $3100 will amount to $3410 at a simple interest of 2% per annum?
(2) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 3% simple interest.
(3) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.
(4) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 9% simple interest?
(5) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $11352 to clear the loan, then find the time period of the loan.
(6) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $8740 to clear the loan, then find the time period of the loan.
(7) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7003 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Karen borrowed a sum of $3950 at 3% simple interest for 3 years.
(9) Mary had to pay $3233 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(10) Calculate the amount due if Mary borrowed a sum of $3050 at 6% simple interest for 4 years.