Simple Interest
Math MCQs

Question :    How much loan did Sarah borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6435 to clear it?

Correct Answer  $5850

Solution & Explanation

Solution

Given,

Amount (A) = $6435

Rate of Simple Interest (R) = 2%

Time (T) = 5 years

Thus, Principal (P) = ?

Method (1) Using Formula

Calculation of the Principal using forumula when Amount, Time and Rate of Simple Interest are given

Formula to find the Principal (P)

Amount (A) = Principal (P) + Principal (P) × Rate (R) × Time (T)

⇒ Amount (A) = Principal (P) [1 + Rate (R) × Time (T)]

⇒ A = P (1 + RT)

Using the formula to find the Amount (A), the fourth can be calculated if any three of A, P, R, and T are given

In the given question, we need to find the Principal (P)

Therefore, by substituting, Amount, Rate, and Time, in the formula A = P (1 + RT) we get

$6435 = P (1 + 2% × 5)

⇒ $6435 = P (1 + ²/₁₀₀ × 5)

⇒ $6435 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $6435 = P (1 + ¹⁰/₁₀₀)

⇒ $6435 = P (^{100 + 10}/₁₀₀)

⇒ $6435 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $6435

⇒ P = ⁶⁴³⁵/_¹¹⁰/100

⇒ P = 6435 × ¹⁰⁰/₁₁₀

⇒ P = ^{6435 × 100}/₁₁₀

⇒ P = ⁶⁴³⁵⁰⁰/₁₁₀

⇒ P = $5850

Thus, the sum borrowed (P) = $5850 Answer

Method (1) Using Unitary Method

Calculation of the Principal using unitary method when Amount, Time and Rate of Simple Interest are given

Calculation of the Simple Interest

Let, the principal = 100

Here, since rate of simple interest = 2% per annum

Thus, Interest = 2% of principal

⇒ Interest = 2% of 100 = 2

Thus, Simple Interest for 1 year = 2

Calculation of the Amount

Since, in the question, time = 5 years

So, we need to calculate the simple interest for the given time period, which is 5 years

Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year

= 5 × 2 = 10

Thus, simple interest for 5 years = 10

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 10 = 110

Calculation of the Principal

Now,

∵ If the Amount is 110, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₀

∴ If the Amount is 6435, then the Principal = ¹⁰⁰/₁₁₀ × 6435

= ^{100 × 6435}/₁₁₀

= ⁶⁴³⁵⁰⁰/₁₁₀

= 5850

Thus, Principal = $5850

Thus, the sum borrowed = $5850 Answer

Similar Questions

(1) Calculate the amount due if David borrowed a sum of $3400 at 2% simple interest for 4 years.

(2) In how much time a principal of $3000 will amount to $3300 at a simple interest of 2% per annum?

(3) Find the amount to be paid if Richard borrowed a sum of $5600 at 8% simple interest for 8 years.

(4) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $8840 to clear the loan, then find the time period of the loan.

(5) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 8% simple interest?

(6) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 5% simple interest.

(7) What amount will be due after 2 years if James borrowed a sum of $3000 at a 8% simple interest?

(8) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 8% simple interest?

(9) Kenneth had to pay $5750 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(10) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 6% simple interest?