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 will be due after 2 years if Matthew borrowed a sum of $3600 at a 7% simple interest?
(2) Find the amount to be paid if Karen borrowed a sum of $5950 at 4% simple interest for 8 years.
(3) Matthew had to pay $4578 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(4) If Jennifer borrowed $3250 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(5) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7700 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 10% simple interest.
(7) What amount does James have to pay after 6 years if he takes a loan of $3000 at 3% simple interest?
(8) John had to pay $3488 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(9) How much loan did Anthony borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7245 to clear it?
(10) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 2% simple interest.