Simple Interest
Math MCQs

Question :    How much loan did Donna borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8562.5 to clear it?

Correct Answer  $6850

Solution & Explanation

Solution

Given,

Amount (A) = $8562.5

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

$8562.5 = P (1 + 5% × 5)

⇒ $8562.5 = P (1 + ⁵/₁₀₀ × 5)

⇒ $8562.5 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $8562.5 = P (1 + ²⁵/₁₀₀)

⇒ $8562.5 = P (^{100 + 25}/₁₀₀)

⇒ $8562.5 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $8562.5

⇒ P = ^8562.5/_¹²⁵/100

⇒ P = 8562.5 × ¹⁰⁰/₁₂₅

⇒ P = ^{8562.5 × 100}/₁₂₅

⇒ P = ⁸⁵⁶²⁵⁰/₁₂₅

⇒ P = $6850

Thus, the sum borrowed (P) = $6850 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 8562.5, then the Principal = ¹⁰⁰/₁₂₅ × 8562.5

= ^{100 × 8562.5}/₁₂₅

= ⁸⁵⁶²⁵⁰/₁₂₅

= 6850

Thus, Principal = $6850

Thus, the sum borrowed = $6850 Answer

Similar Questions

(1) Linda had to pay $3852.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(2) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 8% simple interest.

(3) How much loan did George borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9125 to clear it?

(4) Calculate the amount due if Jessica borrowed a sum of $3750 at 10% simple interest for 3 years.

(5) Charles had to pay $4485 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(6) If Thomas borrowed $3800 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(7) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 2% simple interest?

(8) Calculate the amount due if Linda borrowed a sum of $3350 at 10% simple interest for 3 years.

(9) Find the amount to be paid if David borrowed a sum of $5400 at 6% simple interest for 8 years.

(10) Find the amount to be paid if Linda borrowed a sum of $5350 at 9% simple interest for 7 years.