Question:
What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 9% simple interest?
Correct Answer
$4495
Solution And Explanation
Solution
Given,
Principal (P) = $3100
Rate of Simple Interest (SI) = 9%
Time (t) = 5 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% 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 × 9% × 5
= $3100 ×9/100 × 5
= 3100 × 9 × 5/100
= 27900 × 5/100
= 139500/100
= $1395
Thus, Simple Interest = $1395
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 + $1395
= $4495
Thus, Amount to be paid = $4495 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) = 9%
And, Time (t) = 5 years
Thus, Amount (A)
= $3100 + ($3100 × 9% × 5)
= $3100 + ($3100 ×9/100 × 5)
= $3100 + (3100 × 9 × 5/100)
= $3100 + (27900 × 5/100)
= $3100 + (139500/100)
= $3100 + $1395 = $4495
Thus, Amount (A) to be paid = $4495 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 9%
This, means, $9 per $100 per year
∵ For $100, the simple interest for 1 year = $9
∴ For $1, the simple interest for 1 year = 9/100
∴ For $3100, the simple interest in 1 year
= 9/100 × 3100
= 9 × 3100/100
= 27900/100 = $279
Thus, simple interest for 1 year = $279
Therefore, simple interest for 5 years
= Simple interest for 1 year × 5
= $279 × 5 = $1395
Thus, Simple Interest (SI) = $1395
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3100 + $1395
= $4495
Thus, Amount to be paid = $4495 Answer
Similar Questions
(1) Calculate the amount due if Barbara borrowed a sum of $3550 at 3% simple interest for 4 years.
(2) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.
(3) How much loan did James borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6250 to clear it?
(4) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $11765 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 6% simple interest.
(6) If Barbara borrowed $3550 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(7) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 2% simple interest?
(8) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $9516 to clear the loan, then find the time period of the loan.
(9) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.
(10) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 5% simple interest?