Question:
Find the amount to be paid if Robert borrowed a sum of $5100 at 2% simple interest for 8 years.
Correct Answer
$5916
Solution And Explanation
Solution
Given,
Principal (P) = $5100
Rate of Simple Interest (SI) = 2%
Time (t) = 8 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) = $5100 × 2% × 8
= $5100 ×2/100 × 8
= 5100 × 2 × 8/100
= 10200 × 8/100
= 81600/100
= $816
Thus, Simple Interest = $816
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 = $5100 + $816
= $5916
Thus, Amount to be paid = $5916 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 = $5100
Rate of Simple Interest (SI) or (R) = 2%
And, Time (t) = 8 years
Thus, Amount (A)
= $5100 + ($5100 × 2% × 8)
= $5100 + ($5100 ×2/100 × 8)
= $5100 + (5100 × 2 × 8/100)
= $5100 + (10200 × 8/100)
= $5100 + (81600/100)
= $5100 + $816 = $5916
Thus, Amount (A) to be paid = $5916 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 $5100, the simple interest in 1 year
= 2/100 × 5100
= 2 × 5100/100
= 10200/100 = $102
Thus, simple interest for 1 year = $102
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $102 × 8 = $816
Thus, Simple Interest (SI) = $816
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5100 + $816
= $5916
Thus, Amount to be paid = $5916 Answer
Similar Questions
(1) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $8480 to clear the loan, then find the time period of the loan.
(2) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10492 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Charles borrowed a sum of $5900 at 8% simple interest for 8 years.
(4) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 2% simple interest.
(5) Calculate the amount due if Susan borrowed a sum of $3650 at 3% simple interest for 3 years.
(6) How much loan did Kevin borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8875 to clear it?
(7) Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $9520 to clear the loan, then find the time period of the loan.
(8) What amount will be due after 2 years if John borrowed a sum of $3100 at a 7% simple interest?
(9) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 6% simple interest?
(10) What amount does James have to pay after 5 years if he takes a loan of $3000 at 9% simple interest?