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) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $9412 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 5% simple interest.
(3) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6106 to clear the loan, then find the time period of the loan.
(4) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $8036 to clear the loan, then find the time period of the loan.
(5) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $10318 to clear the loan, then find the time period of the loan.
(6) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $10240 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 6% simple interest.
(8) Donald had to pay $4905 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(9) Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $7140 to clear the loan, then find the time period of the loan.
(10) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $9360 to clear the loan, then find the time period of the loan.