Question:
What amount does David have to pay after 5 years if he takes a loan of $3400 at 10% simple interest?
Correct Answer
$5100
Solution And Explanation
Solution
Given,
Principal (P) = $3400
Rate of Simple Interest (SI) = 10%
Time (t) = 5 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) = $3400 × 10% × 5
= $3400 ×10/100 × 5
= 3400 × 10 × 5/100
= 34000 × 5/100
= 170000/100
= $1700
Thus, Simple Interest = $1700
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 = $3400 + $1700
= $5100
Thus, Amount to be paid = $5100 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 = $3400
Rate of Simple Interest (SI) or (R) = 10%
And, Time (t) = 5 years
Thus, Amount (A)
= $3400 + ($3400 × 10% × 5)
= $3400 + ($3400 ×10/100 × 5)
= $3400 + (3400 × 10 × 5/100)
= $3400 + (34000 × 5/100)
= $3400 + (170000/100)
= $3400 + $1700 = $5100
Thus, Amount (A) to be paid = $5100 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 $3400, the simple interest in 1 year
= 10/100 × 3400
= 10 × 3400/100
= 34000/100 = $340
Thus, simple interest for 1 year = $340
Therefore, simple interest for 5 years
= Simple interest for 1 year × 5
= $340 × 5 = $1700
Thus, Simple Interest (SI) = $1700
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3400 + $1700
= $5100
Thus, Amount to be paid = $5100 Answer
Similar Questions
(1) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $7546 to clear the loan, then find the time period of the loan.
(2) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 6% simple interest?
(3) Calculate the amount due if William borrowed a sum of $3500 at 8% simple interest for 4 years.
(4) How much loan did Margaret borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7302.5 to clear it?
(5) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 3% simple interest.
(6) Find the amount to be paid if Joseph borrowed a sum of $5700 at 5% simple interest for 8 years.
(7) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $9288 to clear the loan, then find the time period of the loan.
(8) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.
(9) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $8688 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if William borrowed a sum of $5500 at 8% simple interest for 8 years.