Question:
What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 8% simple interest?
Correct Answer
$5476
Solution And Explanation
Solution
Given,
Principal (P) = $3700
Rate of Simple Interest (SI) = 8%
Time (t) = 6 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) = $3700 × 8% × 6
= $3700 ×8/100 × 6
= 3700 × 8 × 6/100
= 29600 × 6/100
= 177600/100
= $1776
Thus, Simple Interest = $1776
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 = $3700 + $1776
= $5476
Thus, Amount to be paid = $5476 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 = $3700
Rate of Simple Interest (SI) or (R) = 8%
And, Time (t) = 6 years
Thus, Amount (A)
= $3700 + ($3700 × 8% × 6)
= $3700 + ($3700 ×8/100 × 6)
= $3700 + (3700 × 8 × 6/100)
= $3700 + (29600 × 6/100)
= $3700 + (177600/100)
= $3700 + $1776 = $5476
Thus, Amount (A) to be paid = $5476 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 $3700, the simple interest in 1 year
= 8/100 × 3700
= 8 × 3700/100
= 29600/100 = $296
Thus, simple interest for 1 year = $296
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $296 × 6 = $1776
Thus, Simple Interest (SI) = $1776
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3700 + $1776
= $5476
Thus, Amount to be paid = $5476 Answer
Similar Questions
(1) If Ashley paid $4914 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(2) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $8520 to clear the loan, then find the time period of the loan.
(3) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $8000 to clear the loan, then find the time period of the loan.
(4) Elizabeth had to pay $3967.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(5) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $6808 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Charles borrowed a sum of $5900 at 7% simple interest for 7 years.
(7) Find the amount to be paid if Christopher borrowed a sum of $6000 at 7% simple interest for 7 years.
(8) Find the amount to be paid if Richard borrowed a sum of $5600 at 3% simple interest for 7 years.
(9) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $10540 to clear the loan, then find the time period of the loan.
(10) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 7% simple interest?