Simple Interest
Math MCQs

Question :    In how much time a principal of $3150 will amount to $3622.5 at a simple interest of 5% per annum?

Correct Answer  3

Solution & Explanation

Solution

Given,

Principal (P) = $3150

Rate of Simple Interest (R) = 5% per annum

Amount (A) = $3622.5

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 = $3622.5 – $3150 = $472.5

Thus, Simple Interest = $472.5

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 × 472.5}/_{3150 × 5}

= ⁴⁷²⁵⁰/₁₅₇₅₀

= 3 years (using formula)

Thus, Time (T) = 3 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) = $3150

Rate of Simple Interest (R) = 5% per annum

Simple Interest = $472.5 (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 = 5% of Principal

= 5% of $3150

= ⁵/₁₀₀ × 3150

= ^{5 × 3150}/₁₀₀

= ¹⁵⁷⁵⁰/₁₀₀ = 157.5

Thus, simple Interest for 1 year = $157.5

Now,

∵ If the simple Interest is $157.5, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/_157.5 years

∴ If the simple Interest is $472.5, then the time = ¹/_157.5 × 472.5 years

= ^{1 × 472.5}/_157.5 years

= ^472.5/_157.5 = 3 years

Thus, time (T) = 3 years Answer

Similar Questions

(1) Calculate the amount due if Linda borrowed a sum of $3350 at 2% simple interest for 4 years.

(2) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 6% simple interest.

(3) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 3% simple interest?

(4) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $8046 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due if Susan borrowed a sum of $3650 at 5% simple interest for 4 years.

(6) Calculate the amount due if Christopher borrowed a sum of $4000 at 10% simple interest for 3 years.

(7) How much loan did Jessica borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7187.5 to clear it?

(8) If Jennifer paid $3640 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(9) If Andrew paid $5760 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(10) How much loan did Timothy borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9250 to clear it?