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) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $6708 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 9% simple interest.
(3) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $8804 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Robert borrowed a sum of $5100 at 6% simple interest for 7 years.
(5) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $6314 to clear the loan, then find the time period of the loan.
(6) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $11180 to clear the loan, then find the time period of the loan.
(7) Mary had to pay $3233 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(8) Find the amount to be paid if David borrowed a sum of $5400 at 4% simple interest for 8 years.
(9) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $9600 to clear the loan, then find the time period of the loan.
(10) How much loan did James borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5500 to clear it?