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) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 5% simple interest.
(2) Find the amount to be paid if Christopher borrowed a sum of $6000 at 5% simple interest for 8 years.
(3) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 6% simple interest.
(4) Find the amount to be paid if Barbara borrowed a sum of $5550 at 2% simple interest for 8 years.
(5) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $8008 to clear the loan, then find the time period of the loan.
(6) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $9880 to clear the loan, then find the time period of the loan.
(7) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 4% simple interest?
(8) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 4% simple interest.
(9) 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.
(10) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 2% simple interest.