Simple Interest
Math MCQs

Question :    How much loan did Carol borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8107.5 to clear it?

Correct Answer  $7050

Solution & Explanation

Solution

Given,

Amount (A) = $8107.5

Rate of Simple Interest (R) = 3%

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

$8107.5 = P (1 + 3% × 5)

⇒ $8107.5 = P (1 + ³/₁₀₀ × 5)

⇒ $8107.5 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $8107.5 = P (1 + ¹⁵/₁₀₀)

⇒ $8107.5 = P (^{100 + 15}/₁₀₀)

⇒ $8107.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $8107.5

⇒ P = ^8107.5/_¹¹⁵/100

⇒ P = 8107.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{8107.5 × 100}/₁₁₅

⇒ P = ⁸¹⁰⁷⁵⁰/₁₁₅

⇒ P = $7050

Thus, the sum borrowed (P) = $7050 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 = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

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 × 3 = 15

Thus, simple interest for 5 years = 15

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 15 = 115

Calculation of the Principal

Now,

∵ If the Amount is 115, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₅

∴ If the Amount is 8107.5, then the Principal = ¹⁰⁰/₁₁₅ × 8107.5

= ^{100 × 8107.5}/₁₁₅

= ⁸¹⁰⁷⁵⁰/₁₁₅

= 7050

Thus, Principal = $7050

Thus, the sum borrowed = $7050 Answer

Similar Questions

(1) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 6% simple interest?

(2) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 8% simple interest?

(3) Find the amount to be paid if Karen borrowed a sum of $5950 at 6% simple interest for 7 years.

(4) How much loan did Melissa borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8820 to clear it?

(5) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 3% simple interest?

(6) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 9% simple interest?

(7) How much loan did Donald borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7475 to clear it?

(8) How much loan did Sandra borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8062.5 to clear it?

(9) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 7% simple interest?

(10) How much loan did Melissa borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8452.5 to clear it?