Simple Interest
Math MCQs

Question :    Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $7360 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $4600

Rate of Simple Interest (R) = 10% per annum

Amount (A) = $7360

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 = $7360 – $4600 = $2760

Thus, Simple Interest = $2760

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 × 2760}/_{4600 × 10}

= ²⁷⁶⁰⁰⁰/₄₆₀₀₀

= 6 years (using formula)

Thus, Time (T) = 6 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) = $4600

Rate of Simple Interest (R) = 10% per annum

Simple Interest = $2760 (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 = 10% of Principal

= 10% of $4600

= ¹⁰/₁₀₀ × 4600

= ^{10 × 4600}/₁₀₀

= ⁴⁶⁰⁰⁰/₁₀₀ = 460

Thus, simple Interest for 1 year = $460

Now,

∵ If the simple Interest is $460, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₆₀ years

∴ If the simple Interest is $2760, then the time = ¹/₄₆₀ × 2760 years

= ^{1 × 2760}/₄₆₀ years

= ²⁷⁶⁰/₄₆₀ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) In how much time a principal of $3100 will amount to $3286 at a simple interest of 3% per annum?

(2) Calculate the amount due if Jennifer borrowed a sum of $3250 at 3% simple interest for 4 years.

(3) Find the amount to be paid if Karen borrowed a sum of $5950 at 5% simple interest for 7 years.

(4) Calculate the amount due if William borrowed a sum of $3500 at 9% simple interest for 4 years.

(5) Find the amount to be paid if Richard borrowed a sum of $5600 at 5% simple interest for 8 years.

(6) Find the amount to be paid if Linda borrowed a sum of $5350 at 2% simple interest for 8 years.

(7) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 3% simple interest.

(8) Margaret had to pay $4611 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(9) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.

(10) How much loan did David borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6210 to clear it?