Question:
Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 4% simple interest.
Correct Answer
$7840
Solution And Explanation
Solution
Given,
Principal (P) = $5600
Rate of Simple Interest (SI) = 4%
Time (t) = 10 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) = $5600 × 4% × 10
= $5600 ×4/100 × 10
= 5600 × 4 × 10/100
= 22400 × 10/100
= 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) = 4%
And, Time (t) = 10 years
Thus, Amount (A)
= $5600 + ($5600 × 4% × 10)
= $5600 + ($5600 ×4/100 × 10)
= $5600 + (5600 × 4 × 10/100)
= $5600 + (22400 × 10/100)
= $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 = 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 $5600, the simple interest in 1 year
= 4/100 × 5600
= 4 × 5600/100
= 22400/100 = $224
Thus, simple interest for 1 year = $224
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $224 × 10 = $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) Joseph had to pay $4033 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(2) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 5% simple interest?
(3) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 5% simple interest?
(4) What amount does William have to pay after 6 years if he takes a loan of $3500 at 3% simple interest?
(5) Find the amount to be paid if Michael borrowed a sum of $5300 at 10% simple interest for 8 years.
(6) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $8476 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if Christopher borrowed a sum of $6000 at 4% simple interest for 7 years.
(8) Sarah had to pay $4312 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(9) Find the amount to be paid if Joseph borrowed a sum of $5700 at 10% simple interest for 7 years.
(10) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $9768 to clear the loan, then find the time period of the loan.