Simple Interest
Math MCQs

Question :    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?

Correct Answer  $6450

Solution & Explanation

Solution

Given,

Amount (A) = $8062.5

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

$8062.5 = P (1 + 5% × 5)

⇒ $8062.5 = P (1 + ⁵/₁₀₀ × 5)

⇒ $8062.5 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $8062.5 = P (1 + ²⁵/₁₀₀)

⇒ $8062.5 = P (^{100 + 25}/₁₀₀)

⇒ $8062.5 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $8062.5

⇒ P = ^8062.5/_¹²⁵/100

⇒ P = 8062.5 × ¹⁰⁰/₁₂₅

⇒ P = ^{8062.5 × 100}/₁₂₅

⇒ P = ⁸⁰⁶²⁵⁰/₁₂₅

⇒ P = $6450

Thus, the sum borrowed (P) = $6450 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 8062.5, then the Principal = ¹⁰⁰/₁₂₅ × 8062.5

= ^{100 × 8062.5}/₁₂₅

= ⁸⁰⁶²⁵⁰/₁₂₅

= 6450

Thus, Principal = $6450

Thus, the sum borrowed = $6450 Answer

Similar Questions

(1) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8745 to clear it?

(2) Find the amount to be paid if Joseph borrowed a sum of $5700 at 4% simple interest for 8 years.

(3) 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?

(4) Find the amount to be paid if Susan borrowed a sum of $5650 at 10% simple interest for 8 years.

(5) Calculate the amount due if Mary borrowed a sum of $3050 at 9% simple interest for 3 years.

(6) Calculate the amount due if Barbara borrowed a sum of $3550 at 5% simple interest for 4 years.

(7) In how much time a principal of $3100 will amount to $3410 at a simple interest of 5% per annum?

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

(9) Find the amount to be paid if Linda borrowed a sum of $5350 at 3% simple interest for 7 years.

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