Question:
Calculate the amount due if David borrowed a sum of $3400 at 8% simple interest for 4 years.
Correct Answer
$4488
Solution And Explanation
Solution
Given,
Principal (P) = $3400
Rate of Simple Interest (SI) = 8%
Time (t) = 4 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) = $3400 × 8% × 4
= $3400 ×8/100 × 4
= 3400 × 8 × 4/100
= 27200 × 4/100
= 108800/100
= $1088
Thus, Simple Interest = $1088
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 + $1088
= $4488
Thus, Amount to be paid = $4488 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) = 8%
And, Time (t) = 4 years
Thus, Amount (A)
= $3400 + ($3400 × 8% × 4)
= $3400 + ($3400 ×8/100 × 4)
= $3400 + (3400 × 8 × 4/100)
= $3400 + (27200 × 4/100)
= $3400 + (108800/100)
= $3400 + $1088 = $4488
Thus, Amount (A) to be paid = $4488 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 $3400, the simple interest in 1 year
= 8/100 × 3400
= 8 × 3400/100
= 27200/100 = $272
Thus, simple interest for 1 year = $272
Therefore, simple interest for 4 years
= Simple interest for 1 year × 4
= $272 × 4 = $1088
Thus, Simple Interest (SI) = $1088
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3400 + $1088
= $4488
Thus, Amount to be paid = $4488 Answer
Similar Questions
(1) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $11970 to clear the loan, then find the time period of the loan.
(2) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $11696 to clear the loan, then find the time period of the loan.
(3) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $8470 to clear the loan, then find the time period of the loan.
(4) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 3% simple interest?
(5) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 10% simple interest?
(6) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $6364 to clear the loan, then find the time period of the loan.
(7) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $7052 to clear the loan, then find the time period of the loan.
(8) Susan had to pay $3978.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(9) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $8112 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if Joseph borrowed a sum of $5700 at 6% simple interest for 7 years.