Question:
Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 4% simple interest.
Correct Answer
$7980
Solution And Explanation
Solution
Given,
Principal (P) = $5700
Rate of Simple Interest (SI) = 4%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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) = $5700 × 4% × 10
= $5700 ×4/100 × 10
= 5700 × 4 × 10/100
= 22800 × 10/100
= 228000/100
= $2280
Thus, Simple Interest = $2280
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 = $5700 + $2280
= $7980
Thus, Amount to be paid = $7980 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 = $5700
Rate of Simple Interest (SI) or (R) = 4%
And, Time (t) = 10 years
Thus, Amount (A)
= $5700 + ($5700 × 4% × 10)
= $5700 + ($5700 ×4/100 × 10)
= $5700 + (5700 × 4 × 10/100)
= $5700 + (22800 × 10/100)
= $5700 + (228000/100)
= $5700 + $2280 = $7980
Thus, Amount (A) to be paid = $7980 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $5700, the simple interest in 1 year
= 4/100 × 5700
= 4 × 5700/100
= 22800/100 = $228
Thus, simple interest for 1 year = $228
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $228 × 10 = $2280
Thus, Simple Interest (SI) = $2280
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5700 + $2280
= $7980
Thus, Amount to be paid = $7980 Answer
Similar Questions
(1) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 4% simple interest?
(2) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 9% simple interest.
(3) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $9514 to clear the loan, then find the time period of the loan.
(4) What amount does James have to pay after 5 years if he takes a loan of $3000 at 7% simple interest?
(5) David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Mary borrowed a sum of $5050 at 3% simple interest for 7 years.
(7) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $6864 to clear the loan, then find the time period of the loan.
(8) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $5680 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Joseph borrowed a sum of $3700 at 3% simple interest for 3 years.
(10) Calculate the amount due if William borrowed a sum of $3500 at 3% simple interest for 4 years.