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 does Richard have to pay after 5 years if he takes a loan of $3600 at 8% simple interest?
(2) In how much time a principal of $3050 will amount to $3416 at a simple interest of 3% per annum?
(3) How much loan did Joshua borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7590 to clear it?
(4) Michelle had to pay $5692.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(5) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $9672 to clear the loan, then find the time period of the loan.
(6) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 8% simple interest?
(7) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $7252 to clear the loan, then find the time period of the loan.
(8) David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $7152 to clear the loan, then find the time period of the loan.
(9) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $10132 to clear the loan, then find the time period of the loan.
(10) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 10% simple interest?