Simple Interest
Math MCQs

Question :    Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $5100

Rate of Simple Interest (R) = 6% per annum

Amount (A) = $8160

Thus, time (T) = ?

Method (1) Using Formula

Calculation of Simple Interest, when Principal and Amount are given

Formual to Calculate Simple Interest when Principal and Amount are given

We know that, Amount (A) = Principal (P) + Simple Interest (SI)

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $8160 – $5100 = $3060

Thus, Simple Interest = $3060

Calculation of the Time using forumula when Amount, Simple Interest and Principal are known

Formula to find the Time (T)

Time (T) = ^{100 × Simple Interest}/_{Principal × Rate of Interest}

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 3060}/_{5100 × 6}

= ³⁰⁶⁰⁰⁰/₃₀₆₀₀

= 10 years (using formula)

Thus, Time (T) = 10 years (from time taken before calculation)Answer

Calculation of the Time using Unitary Method when Amount, Simple Interest and Principal are known

Here, we have

Principal (P) = $5100

Rate of Simple Interest (R) = 6% per annum

Simple Interest = $3060 (As calculated above by subtracting Principal from the Amount given)

We know that, interest is calculated on the basis of the Principal.

This means Simple Interest for 1 year = Rate of simple interest × Principal

Thus, Simple Interest for 1 year = 6% of Principal

= 6% of $5100

= ⁶/₁₀₀ × 5100

= ^{6 × 5100}/₁₀₀

= ³⁰⁶⁰⁰/₁₀₀ = 306

Thus, simple Interest for 1 year = $306

Now,

∵ If the simple Interest is $306, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₀₆ years

∴ If the simple Interest is $3060, then the time = ¹/₃₀₆ × 3060 years

= ^{1 × 3060}/₃₀₆ years

= ³⁰⁶⁰/₃₀₆ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) How much loan did Amanda borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8580 to clear it?

(2) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 4% simple interest?

(3) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 10% simple interest?

(4) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 6% simple interest?

(5) If William paid $4200 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(6) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 9% simple interest?

(7) Patricia had to pay $3433.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(8) If Mark paid $5104 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(9) How much loan did Melissa borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8452.5 to clear it?

(10) If Thomas paid $4256 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.