Question:
What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 2% simple interest?
Correct Answer
$3472
Solution And Explanation
Solution
Given,
Principal (P) = $3100
Rate of Simple Interest (SI) = 2%
Time (t) = 6 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 2% simple interest means, Rate of Simple Interest (SI) is 2% 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 × 2% × 6
= $3100 ×2/100 × 6
= 3100 × 2 × 6/100
= 6200 × 6/100
= 37200/100
= $372
Thus, Simple Interest = $372
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 + $372
= $3472
Thus, Amount to be paid = $3472 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) = 2%
And, Time (t) = 6 years
Thus, Amount (A)
= $3100 + ($3100 × 2% × 6)
= $3100 + ($3100 ×2/100 × 6)
= $3100 + (3100 × 2 × 6/100)
= $3100 + (6200 × 6/100)
= $3100 + (37200/100)
= $3100 + $372 = $3472
Thus, Amount (A) to be paid = $3472 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 2%
This, means, $2 per $100 per year
∵ For $100, the simple interest for 1 year = $2
∴ For $1, the simple interest for 1 year = 2/100
∴ For $3100, the simple interest in 1 year
= 2/100 × 3100
= 2 × 3100/100
= 6200/100 = $62
Thus, simple interest for 1 year = $62
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $62 × 6 = $372
Thus, Simple Interest (SI) = $372
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3100 + $372
= $3472
Thus, Amount to be paid = $3472 Answer
Similar Questions
(1) Charles had to pay $4368 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(2) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $9984 to clear the loan, then find the time period of the loan.
(3) What amount does James have to pay after 6 years if he takes a loan of $3000 at 4% simple interest?
(4) Calculate the amount due if Jennifer borrowed a sum of $3250 at 10% simple interest for 4 years.
(5) 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.
(6) How much loan did Anthony borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6930 to clear it?
(7) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 8% simple interest.
(8) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 9% simple interest?
(9) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 6% simple interest?
(10) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 5% simple interest?