Question:
Find the amount to be paid if Robert borrowed a sum of $5100 at 8% simple interest for 8 years.
Correct Answer
$8364
Solution And Explanation
Solution
Given,
Principal (P) = $5100
Rate of Simple Interest (SI) = 8%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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 × 8% × 8
= $5100 ×8/100 × 8
= 5100 × 8 × 8/100
= 40800 × 8/100
= 326400/100
= $3264
Thus, Simple Interest = $3264
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 + $3264
= $8364
Thus, Amount to be paid = $8364 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) = 8%
And, Time (t) = 8 years
Thus, Amount (A)
= $5100 + ($5100 × 8% × 8)
= $5100 + ($5100 ×8/100 × 8)
= $5100 + (5100 × 8 × 8/100)
= $5100 + (40800 × 8/100)
= $5100 + (326400/100)
= $5100 + $3264 = $8364
Thus, Amount (A) to be paid = $8364 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $5100, the simple interest in 1 year
= 8/100 × 5100
= 8 × 5100/100
= 40800/100 = $408
Thus, simple interest for 1 year = $408
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $408 × 8 = $3264
Thus, Simple Interest (SI) = $3264
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5100 + $3264
= $8364
Thus, Amount to be paid = $8364 Answer
Similar Questions
(1) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.
(2) Paul had to pay $5264 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(3) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 8% simple interest?
(4) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $9632 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Mary borrowed a sum of $3050 at 9% simple interest for 4 years.
(6) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $8112 to clear the loan, then find the time period of the loan.
(7) Charles took a loan of $5800 at the rate of 8% simple interest per annum. If he paid an amount of $9512 to clear the loan, then find the time period of the loan.
(8) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $7172 to clear the loan, then find the time period of the loan.
(9) If Mark paid $4752 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(10) Find the amount to be paid if David borrowed a sum of $5400 at 8% simple interest for 8 years.