Simple Interest
Math MCQs

Question :    If Jennifer paid $3770 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $3250

Solution & Explanation

Solution

Given,

Amount (A) = $3770

Rate of Simple Interest (R) = 4%

Time (T) = 4 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

$3770 = P (1 + 4% × 4)

⇒ $3770 = P (1 + ⁴/₁₀₀ × 4)

⇒ $3770 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $3770 = P (1 + ¹⁶/₁₀₀)

⇒ $3770 = P (^{100 + 16}/₁₀₀)

⇒ $3770 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $3770

⇒ P = ³⁷⁷⁰/_¹¹⁶/100

⇒ P = 3770 × ¹⁰⁰/₁₁₆

⇒ P = ^{3770 × 100}/₁₁₆

⇒ P = ³⁷⁷⁰⁰⁰/₁₁₆

⇒ P = $3250

Thus, the sum borrowed (P) = $3250 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 = 4% per annum

Thus, Interest = 4% of principal

⇒ Interest = 4% of 100 = 4

Thus, Simple Interest for 1 year = 4

Calculation of the Amount

Since, in the question, time = 4 years

So, we need to calculate the simple interest for the given time period, which is 4 years

Thus, Simple Interest for 4 years = 4 × Simple Interest for 1 year

= 4 × 4 = 16

Thus, simple interest for 4 years = 16

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 16 = 116

Calculation of the Principal

Now,

∵ If the Amount is 116, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₆

∴ If the Amount is 3770, then the Principal = ¹⁰⁰/₁₁₆ × 3770

= ^{100 × 3770}/₁₁₆

= ³⁷⁷⁰⁰⁰/₁₁₆

= 3250

Thus, Principal = $3250

Thus, the sum borrowed = $3250 Answer

Similar Questions

(1) Michelle had to pay $5395.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(2) In how much time a principal of $3200 will amount to $3840 at a simple interest of 4% per annum?

(3) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $10140 to clear the loan, then find the time period of the loan.

(4) Matthew had to pay $4452 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(5) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 7% simple interest?

(6) If Kenneth paid $5800 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(7) In how much time a principal of $3100 will amount to $3348 at a simple interest of 4% per annum?

(8) Elizabeth had to pay $3864 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(9) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $7568 to clear the loan, then find the time period of the loan.

(10) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $9112 to clear the loan, then find the time period of the loan.