Simple Interest
Math MCQs

Question :    In how much time a principal of $3200 will amount to $3840 at a simple interest of 5% per annum?

Correct Answer  4

Solution & Explanation

Solution

Given,

Principal (P) = $3200

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

Amount (A) = $3840

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 = $3840 – $3200 = $640

Thus, Simple Interest = $640

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 × 640}/_{3200 × 5}

= ⁶⁴⁰⁰⁰/₁₆₀₀₀

= 4 years (using formula)

Thus, Time (T) = 4 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) = $3200

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

Simple Interest = $640 (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 $3200

= ⁵/₁₀₀ × 3200

= ^{5 × 3200}/₁₀₀

= ¹⁶⁰⁰⁰/₁₀₀ = 160

Thus, simple Interest for 1 year = $160

Now,

∵ If the simple Interest is $160, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₁₆₀ years

∴ If the simple Interest is $640, then the time = ¹/₁₆₀ × 640 years

= ^{1 × 640}/₁₆₀ years

= ⁶⁴⁰/₁₆₀ = 4 years

Thus, time (T) = 4 years Answer

Similar Questions

(1) How much loan did Thomas borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7250 to clear it?

(2) If Charles borrowed $3900 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(3) How much loan did Betty borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7500 to clear it?

(4) Find the amount to be paid if Karen borrowed a sum of $5950 at 9% simple interest for 8 years.

(5) Find the amount to be paid if Sarah borrowed a sum of $5850 at 9% simple interest for 8 years.

(6) What amount does James have to pay after 5 years if he takes a loan of $3000 at 5% simple interest?

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

(8) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 4% simple interest?

(9) How much loan did Melissa borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8085 to clear it?

(10) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 5% simple interest.