Simple Interest
Math MCQs

Question :    In how much time a principal of $3200 will amount to $3392 at a simple interest of 2% per annum?

Correct Answer  3

Solution & Explanation

Solution

Given,

Principal (P) = $3200

Rate of Simple Interest (R) = 2% per annum

Amount (A) = $3392

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 = $3392 – $3200 = $192

Thus, Simple Interest = $192

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 × 192}/_{3200 × 2}

= ¹⁹²⁰⁰/₆₄₀₀

= 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) = $3200

Rate of Simple Interest (R) = 2% per annum

Simple Interest = $192 (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 = 2% of Principal

= 2% of $3200

= ²/₁₀₀ × 3200

= ^{2 × 3200}/₁₀₀

= ⁶⁴⁰⁰/₁₀₀ = 64

Thus, simple Interest for 1 year = $64

Now,

∵ If the simple Interest is $64, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₆₄ years

∴ If the simple Interest is $192, then the time = ¹/₆₄ × 192 years

= ^{1 × 192}/₆₄ years

= ¹⁹²/₆₄ = 3 years

Thus, time (T) = 3 years Answer

Similar Questions

(1) Find the amount to be paid if Joseph borrowed a sum of $5700 at 5% simple interest for 8 years.

(2) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $8856 to clear the loan, then find the time period of the loan.

(3) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $7396 to clear the loan, then find the time period of the loan.

(4) What amount does John have to pay after 6 years if he takes a loan of $3200 at 8% simple interest?

(5) Find the amount to be paid if Susan borrowed a sum of $5650 at 5% simple interest for 7 years.

(6) Find the amount to be paid if Sarah borrowed a sum of $5850 at 10% simple interest for 8 years.

(7) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 8% simple interest.

(8) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 7% simple interest?

(9) Paul had to pay $5405 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(10) How much loan did James borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6000 to clear it?