Question:
If Susan borrowed $3650 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
Correct Answer
$3869
Solution And Explanation
Solution
Given,
Principal (P) = $3650
Rate of Simple Interest (SI) = 3%
Time (t) = 2 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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 × 3% × 2
= $3650 ×3/100 × 2
= 3650 × 3 × 2/100
= 10950 × 2/100
= 21900/100
= $219
Thus, Simple Interest = $219
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 + $219
= $3869
Thus, Amount to be paid = $3869 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) = 3%
And, Time (t) = 2 years
Thus, Amount (A)
= $3650 + ($3650 × 3% × 2)
= $3650 + ($3650 ×3/100 × 2)
= $3650 + (3650 × 3 × 2/100)
= $3650 + (10950 × 2/100)
= $3650 + (21900/100)
= $3650 + $219 = $3869
Thus, Amount (A) to be paid = $3869 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $3650, the simple interest in 1 year
= 3/100 × 3650
= 3 × 3650/100
= 10950/100 = $109.5
Thus, simple interest for 1 year = $109.5
Therefore, simple interest for 2 years
= Simple interest for 1 year × 2
= $109.5 × 2 = $219
Thus, Simple Interest (SI) = $219
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3650 + $219
= $3869
Thus, Amount to be paid = $3869 Answer
Similar Questions
(1) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $8436 to clear the loan, then find the time period of the loan.
(2) In how much time a principal of $3200 will amount to $3328 at a simple interest of 2% per annum?
(3) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $5920 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if Jennifer borrowed a sum of $3250 at 6% simple interest for 4 years.
(5) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 10% simple interest.
(6) How much loan did Jacob borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9200 to clear it?
(7) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 10% simple interest?
(8) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 2% simple interest.
(9) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 5% simple interest.
(10) If Andrew paid $5184 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.