Question:
Calculate the amount due if Patricia borrowed a sum of $3150 at 6% simple interest for 4 years.
Correct Answer
$3906
Solution And Explanation
Solution
Given,
Principal (P) = $3150
Rate of Simple Interest (SI) = 6%
Time (t) = 4 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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) = $3150 × 6% × 4
= $3150 ×6/100 × 4
= 3150 × 6 × 4/100
= 18900 × 4/100
= 75600/100
= $756
Thus, Simple Interest = $756
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 = $3150 + $756
= $3906
Thus, Amount to be paid = $3906 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 = $3150
Rate of Simple Interest (SI) or (R) = 6%
And, Time (t) = 4 years
Thus, Amount (A)
= $3150 + ($3150 × 6% × 4)
= $3150 + ($3150 ×6/100 × 4)
= $3150 + (3150 × 6 × 4/100)
= $3150 + (18900 × 4/100)
= $3150 + (75600/100)
= $3150 + $756 = $3906
Thus, Amount (A) to be paid = $3906 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $3150, the simple interest in 1 year
= 6/100 × 3150
= 6 × 3150/100
= 18900/100 = $189
Thus, simple interest for 1 year = $189
Therefore, simple interest for 4 years
= Simple interest for 1 year × 4
= $189 × 4 = $756
Thus, Simple Interest (SI) = $756
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3150 + $756
= $3906
Thus, Amount to be paid = $3906 Answer
Similar Questions
(1) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 7% simple interest for 4 years.
(2) Calculate the amount due if David borrowed a sum of $3400 at 2% simple interest for 4 years.
(3) How much loan did Richard borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6440 to clear it?
(4) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 8% simple interest?
(5) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $7480 to clear the loan, then find the time period of the loan.
(6) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $9350 to clear the loan, then find the time period of the loan.
(7) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $9280 to clear the loan, then find the time period of the loan.
(8) How much loan did Linda borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6420 to clear it?
(9) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $7360 to clear the loan, then find the time period of the loan.
(10) How much loan did Timothy borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8140 to clear it?