Question:
What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 3% simple interest?
Correct Answer
$3565
Solution And Explanation
Solution
Given,
Principal (P) = $3100
Rate of Simple Interest (SI) = 3%
Time (t) = 5 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) = $3100 × 3% × 5
= $3100 ×3/100 × 5
= 3100 × 3 × 5/100
= 9300 × 5/100
= 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) = 3%
And, Time (t) = 5 years
Thus, Amount (A)
= $3100 + ($3100 × 3% × 5)
= $3100 + ($3100 ×3/100 × 5)
= $3100 + (3100 × 3 × 5/100)
= $3100 + (9300 × 5/100)
= $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 = 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 $3100, the simple interest in 1 year
= 3/100 × 3100
= 3 × 3100/100
= 9300/100 = $93
Thus, simple interest for 1 year = $93
Therefore, simple interest for 5 years
= Simple interest for 1 year × 5
= $93 × 5 = $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) Find the amount to be paid if William borrowed a sum of $5500 at 8% simple interest for 8 years.
(2) How much loan did Anthony borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6930 to clear it?
(3) What amount will be due after 2 years if David borrowed a sum of $3200 at a 8% simple interest?
(4) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 4% simple interest.
(5) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 3% simple interest?
(6) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $7520 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if William borrowed a sum of $5500 at 5% simple interest for 8 years.
(8) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $8892 to clear the loan, then find the time period of the loan.
(9) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $7224 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 5% simple interest for 8 years.