Question:
What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 3% simple interest?
Correct Answer
$3658
Solution And Explanation
Solution
Given,
Principal (P) = $3100
Rate of Simple Interest (SI) = 3%
Time (t) = 6 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% × 6
= $3100 ×3/100 × 6
= 3100 × 3 × 6/100
= 9300 × 6/100
= 55800/100
= $558
Thus, Simple Interest = $558
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 + $558
= $3658
Thus, Amount to be paid = $3658 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) = 6 years
Thus, Amount (A)
= $3100 + ($3100 × 3% × 6)
= $3100 + ($3100 ×3/100 × 6)
= $3100 + (3100 × 3 × 6/100)
= $3100 + (9300 × 6/100)
= $3100 + (55800/100)
= $3100 + $558 = $3658
Thus, Amount (A) to be paid = $3658 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 6 years
= Simple interest for 1 year × 6
= $93 × 6 = $558
Thus, Simple Interest (SI) = $558
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3100 + $558
= $3658
Thus, Amount to be paid = $3658 Answer
Similar Questions
(1) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 6% simple interest?
(2) If Paul paid $5640 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(3) In how much time a principal of $3100 will amount to $3348 at a simple interest of 2% per annum?
(4) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $9940 to clear the loan, then find the time period of the loan.
(5) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 4% simple interest?
(6) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $8195 to clear the loan, then find the time period of the loan.
(7) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $8946 to clear the loan, then find the time period of the loan.
(8) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $8424 to clear the loan, then find the time period of the loan.
(9) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.
(10) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 8% simple interest?