Question:
What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 6% simple interest?
Correct Answer
$4216
Solution And Explanation
Solution
Given,
Principal (P) = $3100
Rate of Simple Interest (SI) = 6%
Time (t) = 6 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) = $3100 × 6% × 6
= $3100 ×6/100 × 6
= 3100 × 6 × 6/100
= 18600 × 6/100
= 111600/100
= $1116
Thus, Simple Interest = $1116
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 + $1116
= $4216
Thus, Amount to be paid = $4216 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) = 6%
And, Time (t) = 6 years
Thus, Amount (A)
= $3100 + ($3100 × 6% × 6)
= $3100 + ($3100 ×6/100 × 6)
= $3100 + (3100 × 6 × 6/100)
= $3100 + (18600 × 6/100)
= $3100 + (111600/100)
= $3100 + $1116 = $4216
Thus, Amount (A) to be paid = $4216 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 $3100, the simple interest in 1 year
= 6/100 × 3100
= 6 × 3100/100
= 18600/100 = $186
Thus, simple interest for 1 year = $186
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $186 × 6 = $1116
Thus, Simple Interest (SI) = $1116
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3100 + $1116
= $4216
Thus, Amount to be paid = $4216 Answer
Similar Questions
(1) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $11524 to clear the loan, then find the time period of the loan.
(2) If Sarah paid $4620 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(3) What amount does James have to pay after 6 years if he takes a loan of $3000 at 10% simple interest?
(4) If Matthew paid $4536 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(5) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 7% simple interest.
(6) If Jessica borrowed $3750 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(7) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $6520 to clear the loan, then find the time period of the loan.
(8) How much loan did Sandra borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7095 to clear it?
(9) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $7844 to clear the loan, then find the time period of the loan.
(10) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $9500 to clear the loan, then find the time period of the loan.