Question:
What amount does David have to pay after 6 years if he takes a loan of $3400 at 5% simple interest?
Correct Answer
$4420
Solution And Explanation
Solution
Given,
Principal (P) = $3400
Rate of Simple Interest (SI) = 5%
Time (t) = 6 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 6
= $3400 ×5/100 × 6
= 3400 × 5 × 6/100
= 17000 × 6/100
= 102000/100
= $1020
Thus, Simple Interest = $1020
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 + $1020
= $4420
Thus, Amount to be paid = $4420 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) = 5%
And, Time (t) = 6 years
Thus, Amount (A)
= $3400 + ($3400 × 5% × 6)
= $3400 + ($3400 ×5/100 × 6)
= $3400 + (3400 × 5 × 6/100)
= $3400 + (17000 × 6/100)
= $3400 + (102000/100)
= $3400 + $1020 = $4420
Thus, Amount (A) to be paid = $4420 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $3400, the simple interest in 1 year
= 5/100 × 3400
= 5 × 3400/100
= 17000/100 = $170
Thus, simple interest for 1 year = $170
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $170 × 6 = $1020
Thus, Simple Interest (SI) = $1020
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3400 + $1020
= $4420
Thus, Amount to be paid = $4420 Answer
Similar Questions
(1) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 4% simple interest?
(2) What amount does William have to pay after 6 years if he takes a loan of $3500 at 5% simple interest?
(3) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.
(4) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $7956 to clear the loan, then find the time period of the loan.
(5) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 10% simple interest?
(6) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $7310 to clear the loan, then find the time period of the loan.
(7) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $10064 to clear the loan, then find the time period of the loan.
(8) How much loan did Elizabeth borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5995 to clear it?
(9) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 3% simple interest.
(10) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $8946 to clear the loan, then find the time period of the loan.