Simple Interest
Math MCQs

Question :    In how much time a principal of $3100 will amount to $3379 at a simple interest of 3% per annum?

Correct Answer  3

Solution & Explanation

Solution

Given,

Principal (P) = $3100

Rate of Simple Interest (R) = 3% per annum

Amount (A) = $3379

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 = $3379 – $3100 = $279

Thus, Simple Interest = $279

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 × 279}/_{3100 × 3}

= ²⁷⁹⁰⁰/₉₃₀₀

= 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) = $3100

Rate of Simple Interest (R) = 3% per annum

Simple Interest = $279 (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 = 3% of Principal

= 3% of $3100

= ³/₁₀₀ × 3100

= ^{3 × 3100}/₁₀₀

= ⁹³⁰⁰/₁₀₀ = 93

Thus, simple Interest for 1 year = $93

Now,

∵ If the simple Interest is $93, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₉₃ years

∴ If the simple Interest is $279, then the time = ¹/₉₃ × 279 years

= ^{1 × 279}/₉₃ years

= ²⁷⁹/₉₃ = 3 years

Thus, time (T) = 3 years Answer

Similar Questions

(1) Kimberly had to pay $5208 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(2) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $10764 to clear the loan, then find the time period of the loan.

(3) How much loan did Betty borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7812.5 to clear it?

(4) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 10% simple interest?

(5) How much loan did Sandra borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8062.5 to clear it?

(6) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $8600 to clear the loan, then find the time period of the loan.

(7) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $8162 to clear the loan, then find the time period of the loan.

(8) Find the amount to be paid if Robert borrowed a sum of $5100 at 6% simple interest for 7 years.

(9) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $11247 to clear the loan, then find the time period of the loan.

(10) If Karen paid $4740 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.