Simple Interest
Math MCQs

Question :    How much loan did Michael borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6625 to clear it?

Correct Answer  $5300

Solution & Explanation

Solution

Given,

Amount (A) = $6625

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

$6625 = P (1 + 5% × 5)

⇒ $6625 = P (1 + ⁵/₁₀₀ × 5)

⇒ $6625 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $6625 = P (1 + ²⁵/₁₀₀)

⇒ $6625 = P (^{100 + 25}/₁₀₀)

⇒ $6625 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $6625

⇒ P = ⁶⁶²⁵/_¹²⁵/100

⇒ P = 6625 × ¹⁰⁰/₁₂₅

⇒ P = ^{6625 × 100}/₁₂₅

⇒ P = ⁶⁶²⁵⁰⁰/₁₂₅

⇒ P = $5300

Thus, the sum borrowed (P) = $5300 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 6625, then the Principal = ¹⁰⁰/₁₂₅ × 6625

= ^{100 × 6625}/₁₂₅

= ⁶⁶²⁵⁰⁰/₁₂₅

= 5300

Thus, Principal = $5300

Thus, the sum borrowed = $5300 Answer

Similar Questions

(1) What amount does David have to pay after 5 years if he takes a loan of $3400 at 4% simple interest?

(2) Find the amount to be paid if Thomas borrowed a sum of $5800 at 6% simple interest for 8 years.

(3) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 6% simple interest?

(4) Calculate the amount due if Christopher borrowed a sum of $4000 at 9% simple interest for 4 years.

(5) Calculate the amount due if Charles borrowed a sum of $3900 at 5% simple interest for 4 years.

(6) Find the amount to be paid if Jessica borrowed a sum of $5750 at 2% simple interest for 7 years.

(7) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $11590 to clear the loan, then find the time period of the loan.

(8) Find the amount to be paid if Susan borrowed a sum of $5650 at 6% simple interest for 8 years.

(9) How much loan did Jason borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8855 to clear it?

(10) If Anthony paid $4816 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.