Question:
What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 10% simple interest?
Correct Answer
$5920
Solution And Explanation
Solution
Given,
Principal (P) = $3700
Rate of Simple Interest (SI) = 10%
Time (t) = 6 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 6
= $3700 ×10/100 × 6
= 3700 × 10 × 6/100
= 37000 × 6/100
= 222000/100
= $2220
Thus, Simple Interest = $2220
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 + $2220
= $5920
Thus, Amount to be paid = $5920 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) = 10%
And, Time (t) = 6 years
Thus, Amount (A)
= $3700 + ($3700 × 10% × 6)
= $3700 + ($3700 ×10/100 × 6)
= $3700 + (3700 × 10 × 6/100)
= $3700 + (37000 × 6/100)
= $3700 + (222000/100)
= $3700 + $2220 = $5920
Thus, Amount (A) to be paid = $5920 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $3700, the simple interest in 1 year
= 10/100 × 3700
= 10 × 3700/100
= 37000/100 = $370
Thus, simple interest for 1 year = $370
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $370 × 6 = $2220
Thus, Simple Interest (SI) = $2220
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3700 + $2220
= $5920
Thus, Amount to be paid = $5920 Answer
Similar Questions
(1) Find the amount to be paid if William borrowed a sum of $5500 at 8% simple interest for 7 years.
(2) How much loan did Carol borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8460 to clear it?
(3) Find the amount to be paid if Karen borrowed a sum of $5950 at 10% simple interest for 8 years.
(4) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $10836 to clear the loan, then find the time period of the loan.
(5) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $11584 to clear the loan, then find the time period of the loan.
(6) What amount does David have to pay after 5 years if he takes a loan of $3400 at 2% simple interest?
(7) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 6% simple interest?
(8) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 5% simple interest.
(9) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $7964 to clear the loan, then find the time period of the loan.
(10) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 2% simple interest?