Question:
What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 10% simple interest?
Correct Answer
$4960
Solution And Explanation
Solution
Given,
Principal (P) = $3100
Rate of Simple Interest (SI) = 10%
Time (t) = 6 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 6
= $3100 ×10/100 × 6
= 3100 × 10 × 6/100
= 31000 × 6/100
= 186000/100
= $1860
Thus, Simple Interest = $1860
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 + $1860
= $4960
Thus, Amount to be paid = $4960 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) = 10%
And, Time (t) = 6 years
Thus, Amount (A)
= $3100 + ($3100 × 10% × 6)
= $3100 + ($3100 ×10/100 × 6)
= $3100 + (3100 × 10 × 6/100)
= $3100 + (31000 × 6/100)
= $3100 + (186000/100)
= $3100 + $1860 = $4960
Thus, Amount (A) to be paid = $4960 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $3100, the simple interest in 1 year
= 10/100 × 3100
= 10 × 3100/100
= 31000/100 = $310
Thus, simple interest for 1 year = $310
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $310 × 6 = $1860
Thus, Simple Interest (SI) = $1860
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3100 + $1860
= $4960
Thus, Amount to be paid = $4960 Answer
Similar Questions
(1) What amount does David have to pay after 5 years if he takes a loan of $3400 at 5% simple interest?
(2) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $9916 to clear the loan, then find the time period of the loan.
(3) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $8428 to clear the loan, then find the time period of the loan.
(4) How much loan did Christopher borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7200 to clear it?
(5) How much loan did James borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5500 to clear it?
(6) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 10% simple interest.
(7) Calculate the amount due if David borrowed a sum of $3400 at 5% simple interest for 4 years.
(8) Calculate the amount due if Michael borrowed a sum of $3300 at 7% simple interest for 4 years.
(9) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $9955 to clear the loan, then find the time period of the loan.
(10) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $10540 to clear the loan, then find the time period of the loan.