Simple Interest
Math MCQs

Question :    How much loan did Nancy borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7687.5 to clear it?

Correct Answer  $6150

Solution & Explanation

Solution

Given,

Amount (A) = $7687.5

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

$7687.5 = P (1 + 5% × 5)

⇒ $7687.5 = P (1 + ⁵/₁₀₀ × 5)

⇒ $7687.5 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $7687.5 = P (1 + ²⁵/₁₀₀)

⇒ $7687.5 = P (^{100 + 25}/₁₀₀)

⇒ $7687.5 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $7687.5

⇒ P = ^7687.5/_¹²⁵/100

⇒ P = 7687.5 × ¹⁰⁰/₁₂₅

⇒ P = ^{7687.5 × 100}/₁₂₅

⇒ P = ⁷⁶⁸⁷⁵⁰/₁₂₅

⇒ P = $6150

Thus, the sum borrowed (P) = $6150 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 7687.5, then the Principal = ¹⁰⁰/₁₂₅ × 7687.5

= ^{100 × 7687.5}/₁₂₅

= ⁷⁶⁸⁷⁵⁰/₁₂₅

= 6150

Thus, Principal = $6150

Thus, the sum borrowed = $6150 Answer

Similar Questions

(1) Find the amount to be paid if Thomas borrowed a sum of $5800 at 5% simple interest for 7 years.

(2) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 4% simple interest?

(3) Joseph had to pay $4033 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(4) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 6% simple interest?

(5) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 2% simple interest.

(6) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 6% simple interest?

(7) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 7% simple interest?

(8) Find the amount to be paid if James borrowed a sum of $5000 at 8% simple interest for 7 years.

(9) Calculate the amount due if Robert borrowed a sum of $3100 at 3% simple interest for 3 years.

(10) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 4% simple interest?