Question:
What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 5% simple interest?
Correct Answer
$3875
Solution And Explanation
Solution
Given,
Principal (P) = $3100
Rate of Simple Interest (SI) = 5%
Time (t) = 5 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% × 5
= $3100 ×5/100 × 5
= 3100 × 5 × 5/100
= 15500 × 5/100
= 77500/100
= $775
Thus, Simple Interest = $775
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 + $775
= $3875
Thus, Amount to be paid = $3875 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) = 5 years
Thus, Amount (A)
= $3100 + ($3100 × 5% × 5)
= $3100 + ($3100 ×5/100 × 5)
= $3100 + (3100 × 5 × 5/100)
= $3100 + (15500 × 5/100)
= $3100 + (77500/100)
= $3100 + $775 = $3875
Thus, Amount (A) to be paid = $3875 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 5 years
= Simple interest for 1 year × 5
= $155 × 5 = $775
Thus, Simple Interest (SI) = $775
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3100 + $775
= $3875
Thus, Amount to be paid = $3875 Answer
Similar Questions
(1) Find the amount to be paid if John borrowed a sum of $5200 at 5% simple interest for 8 years.
(2) In how much time a principal of $3100 will amount to $3565 at a simple interest of 5% per annum?
(3) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $11868 to clear the loan, then find the time period of the loan.
(4) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $11020 to clear the loan, then find the time period of the loan.
(5) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $9460 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if John borrowed a sum of $5200 at 3% simple interest for 8 years.
(7) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 3% simple interest.
(8) Barbara had to pay $4082.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(9) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.
(10) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 6% simple interest?