Question:
Calculate the amount due if Robert borrowed a sum of $3100 at 5% simple interest for 3 years.
Correct Answer
$3565
Solution And Explanation
Solution
Given,
Principal (P) = $3100
Rate of Simple Interest (SI) = 5%
Time (t) = 3 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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) = $3100 × 5% × 3
= $3100 ×5/100 × 3
= 3100 × 5 × 3/100
= 15500 × 3/100
= 46500/100
= $465
Thus, Simple Interest = $465
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 = $3100 + $465
= $3565
Thus, Amount to be paid = $3565 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 = $3100
Rate of Simple Interest (SI) or (R) = 5%
And, Time (t) = 3 years
Thus, Amount (A)
= $3100 + ($3100 × 5% × 3)
= $3100 + ($3100 ×5/100 × 3)
= $3100 + (3100 × 5 × 3/100)
= $3100 + (15500 × 3/100)
= $3100 + (46500/100)
= $3100 + $465 = $3565
Thus, Amount (A) to be paid = $3565 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $3100, the simple interest in 1 year
= 5/100 × 3100
= 5 × 3100/100
= 15500/100 = $155
Thus, simple interest for 1 year = $155
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $155 × 3 = $465
Thus, Simple Interest (SI) = $465
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3100 + $465
= $3565
Thus, Amount to be paid = $3565 Answer
Similar Questions
(1) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $6664 to clear the loan, then find the time period of the loan.
(2) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $6956 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Michael borrowed a sum of $3300 at 6% simple interest for 4 years.
(4) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $9916 to clear the loan, then find the time period of the loan.
(5) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 5% simple interest?
(6) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.
(7) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 6% simple interest?
(8) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $10400 to clear the loan, then find the time period of the loan.
(9) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $10148 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if Patricia borrowed a sum of $5150 at 5% simple interest for 8 years.