Question:
Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 10% simple interest.
Correct Answer
$11300
Solution And Explanation
Solution
Given,
Principal (P) = $5650
Rate of Simple Interest (SI) = 10%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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) = $5650 × 10% × 10
= $5650 ×10/100 × 10
= 5650 × 10 × 10/100
= 56500 × 10/100
= 565000/100
= $5650
Thus, Simple Interest = $5650
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 = $5650 + $5650
= $11300
Thus, Amount to be paid = $11300 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 = $5650
Rate of Simple Interest (SI) or (R) = 10%
And, Time (t) = 10 years
Thus, Amount (A)
= $5650 + ($5650 × 10% × 10)
= $5650 + ($5650 ×10/100 × 10)
= $5650 + (5650 × 10 × 10/100)
= $5650 + (56500 × 10/100)
= $5650 + (565000/100)
= $5650 + $5650 = $11300
Thus, Amount (A) to be paid = $11300 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $5650, the simple interest in 1 year
= 10/100 × 5650
= 10 × 5650/100
= 56500/100 = $565
Thus, simple interest for 1 year = $565
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $565 × 10 = $5650
Thus, Simple Interest (SI) = $5650
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5650 + $5650
= $11300
Thus, Amount to be paid = $11300 Answer
Similar Questions
(1) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 10% simple interest?
(2) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $8200 to clear the loan, then find the time period of the loan.
(3) Michelle had to pay $5247 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(4) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 6% simple interest?
(5) James had to pay $3180 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(6) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 2% simple interest?
(7) In how much time a principal of $3200 will amount to $3520 at a simple interest of 2% per annum?
(8) Find the amount to be paid if William borrowed a sum of $5500 at 8% simple interest for 8 years.
(9) If Susan paid $4380 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(10) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $6808 to clear the loan, then find the time period of the loan.