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) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 7% simple interest?
(2) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 7% simple interest.
(3) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $9348 to clear the loan, then find the time period of the loan.
(4) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $11520 to clear the loan, then find the time period of the loan.
(5) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 6% simple interest?
(6) Calculate the amount due if Richard borrowed a sum of $3600 at 6% simple interest for 4 years.
(7) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 8% simple interest?
(8) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 10% simple interest.
(9) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $13000 to clear the loan, then find the time period of the loan.
(10) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 7% simple interest?