Simple Interest
Math MCQs

Question :    How much loan did Susan borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7062.5 to clear it?

Correct Answer  $5650

Solution & Explanation

Solution

Given,

Amount (A) = $7062.5

Rate of Simple Interest (R) = 5%

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

$7062.5 = P (1 + 5% × 5)

⇒ $7062.5 = P (1 + ⁵/₁₀₀ × 5)

⇒ $7062.5 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $7062.5 = P (1 + ²⁵/₁₀₀)

⇒ $7062.5 = P (^{100 + 25}/₁₀₀)

⇒ $7062.5 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $7062.5

⇒ P = ^7062.5/_¹²⁵/100

⇒ P = 7062.5 × ¹⁰⁰/₁₂₅

⇒ P = ^{7062.5 × 100}/₁₂₅

⇒ P = ⁷⁰⁶²⁵⁰/₁₂₅

⇒ P = $5650

Thus, the sum borrowed (P) = $5650 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 = 5% per annum

Thus, Interest = 5% of principal

⇒ Interest = 5% of 100 = 5

Thus, Simple Interest for 1 year = 5

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 × 5 = 25

Thus, simple interest for 5 years = 25

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 25 = 125

Calculation of the Principal

Now,

∵ If the Amount is 125, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₅

∴ If the Amount is 7062.5, then the Principal = ¹⁰⁰/₁₂₅ × 7062.5

= ^{100 × 7062.5}/₁₂₅

= ⁷⁰⁶²⁵⁰/₁₂₅

= 5650

Thus, Principal = $5650

Thus, the sum borrowed = $5650 Answer

Similar Questions

(1) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 7% simple interest.

(2) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 10% simple interest?

(3) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 4% simple interest?

(4) In how much time a principal of $3100 will amount to $3410 at a simple interest of 2% per annum?

(5) Find the amount to be paid if Joseph borrowed a sum of $5700 at 2% simple interest for 7 years.

(6) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 4% simple interest.

(7) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 2% simple interest.

(8) Find the amount to be paid if David borrowed a sum of $5400 at 5% simple interest for 8 years.

(9) In how much time a principal of $3150 will amount to $3654 at a simple interest of 4% per annum?

(10) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 9% simple interest?