Question:
Calculate the amount due if Susan borrowed a sum of $3650 at 10% simple interest for 4 years.
Correct Answer
$5110
Solution And Explanation
Solution
Given,
Principal (P) = $3650
Rate of Simple Interest (SI) = 10%
Time (t) = 4 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) = $3650 × 10% × 4
= $3650 ×10/100 × 4
= 3650 × 10 × 4/100
= 36500 × 4/100
= 146000/100
= $1460
Thus, Simple Interest = $1460
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 = $3650 + $1460
= $5110
Thus, Amount to be paid = $5110 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 = $3650
Rate of Simple Interest (SI) or (R) = 10%
And, Time (t) = 4 years
Thus, Amount (A)
= $3650 + ($3650 × 10% × 4)
= $3650 + ($3650 ×10/100 × 4)
= $3650 + (3650 × 10 × 4/100)
= $3650 + (36500 × 4/100)
= $3650 + (146000/100)
= $3650 + $1460 = $5110
Thus, Amount (A) to be paid = $5110 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 $3650, the simple interest in 1 year
= 10/100 × 3650
= 10 × 3650/100
= 36500/100 = $365
Thus, simple interest for 1 year = $365
Therefore, simple interest for 4 years
= Simple interest for 1 year × 4
= $365 × 4 = $1460
Thus, Simple Interest (SI) = $1460
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3650 + $1460
= $5110
Thus, Amount to be paid = $5110 Answer
Similar Questions
(1) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 6% simple interest?
(2) Find the amount to be paid if Patricia borrowed a sum of $5150 at 2% simple interest for 7 years.
(3) Kimberly had to pay $5347.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(4) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $11900 to clear the loan, then find the time period of the loan.
(5) In how much time a principal of $3150 will amount to $3402 at a simple interest of 2% per annum?
(6) Find the amount to be paid if David borrowed a sum of $5400 at 9% simple interest for 8 years.
(7) Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $6846 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 9% simple interest.
(9) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $8036 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if Susan borrowed a sum of $5650 at 10% simple interest for 8 years.