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) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $6407 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 8% simple interest.
(3) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $12060 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if Karen borrowed a sum of $3950 at 9% simple interest for 4 years.
(5) What amount does David have to pay after 5 years if he takes a loan of $3400 at 3% simple interest?
(6) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 7% simple interest?
(7) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $10626 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if David borrowed a sum of $3400 at 5% simple interest for 4 years.
(9) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $8550 to clear the loan, then find the time period of the loan.
(10) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $11590 to clear the loan, then find the time period of the loan.