Question:
Calculate the amount due if Barbara borrowed a sum of $3550 at 3% simple interest for 3 years.
Correct Answer
$3869.5
Solution And Explanation
Solution
Given,
Principal (P) = $3550
Rate of Simple Interest (SI) = 3%
Time (t) = 3 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) = $3550 × 3% × 3
= $3550 ×3/100 × 3
= 3550 × 3 × 3/100
= 10650 × 3/100
= 31950/100
= $319.5
Thus, Simple Interest = $319.5
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 = $3550 + $319.5
= $3869.5
Thus, Amount to be paid = $3869.5 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 = $3550
Rate of Simple Interest (SI) or (R) = 3%
And, Time (t) = 3 years
Thus, Amount (A)
= $3550 + ($3550 × 3% × 3)
= $3550 + ($3550 ×3/100 × 3)
= $3550 + (3550 × 3 × 3/100)
= $3550 + (10650 × 3/100)
= $3550 + (31950/100)
= $3550 + $319.5 = $3869.5
Thus, Amount (A) to be paid = $3869.5 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 $3550, the simple interest in 1 year
= 3/100 × 3550
= 3 × 3550/100
= 10650/100 = $106.5
Thus, simple interest for 1 year = $106.5
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $106.5 × 3 = $319.5
Thus, Simple Interest (SI) = $319.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3550 + $319.5
= $3869.5
Thus, Amount to be paid = $3869.5 Answer
Similar Questions
(1) In how much time a principal of $3150 will amount to $3654 at a simple interest of 4% per annum?
(2) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 4% simple interest.
(3) Find the amount to be paid if James borrowed a sum of $5000 at 6% simple interest for 7 years.
(4) Calculate the amount due if Mary borrowed a sum of $3050 at 4% simple interest for 3 years.
(5) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 8% simple interest?
(6) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $9000 to clear the loan, then find the time period of the loan.
(7) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 10% simple interest?
(8) 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.
(9) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $6400 to clear the loan, then find the time period of the loan.
(10) If William paid $3920 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.