Simple Interest
Math MCQs

Question :    In how much time a principal of $3200 will amount to $3456 at a simple interest of 4% per annum?

Correct Answer  2

Solution & Explanation

Solution

Given,

Principal (P) = $3200

Rate of Simple Interest (R) = 4% per annum

Amount (A) = $3456

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 = $3456 – $3200 = $256

Thus, Simple Interest = $256

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 × 256}/_{3200 × 4}

= ²⁵⁶⁰⁰/₁₂₈₀₀

= 2 years (using formula)

Thus, Time (T) = 2 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) = 4% per annum

Simple Interest = $256 (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 = 4% of Principal

= 4% of $3200

= ⁴/₁₀₀ × 3200

= ^{4 × 3200}/₁₀₀

= ¹²⁸⁰⁰/₁₀₀ = 128

Thus, simple Interest for 1 year = $128

Now,

∵ If the simple Interest is $128, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₁₂₈ years

∴ If the simple Interest is $256, then the time = ¹/₁₂₈ × 256 years

= ^{1 × 256}/₁₂₈ years

= ²⁵⁶/₁₂₈ = 2 years

Thus, time (T) = 2 years Answer

Similar Questions

(1) Find the amount to be paid if Patricia borrowed a sum of $5150 at 9% simple interest for 7 years.

(2) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $6528 to clear the loan, then find the time period of the loan.

(3) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $9460 to clear the loan, then find the time period of the loan.

(4) If Margaret paid $4698 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(5) Find the amount to be paid if Joseph borrowed a sum of $5700 at 3% simple interest for 8 years.

(6) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 4% simple interest?

(7) What amount does James have to pay after 6 years if he takes a loan of $3000 at 9% simple interest?

(8) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $11780 to clear the loan, then find the time period of the loan.

(9) Find the amount to be paid if Linda borrowed a sum of $5350 at 3% simple interest for 8 years.

(10) Find the amount to be paid if Susan borrowed a sum of $5650 at 3% simple interest for 8 years.