Simple Interest
Math MCQs

Question :    Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $6532 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) = 7% per annum

Amount (A) = $6532

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 = $6532 – $4600 = $1932

Thus, Simple Interest = $1932

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 × 1932}/_{4600 × 7}

= ¹⁹³²⁰⁰/₃₂₂₀₀

= 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) = 7% per annum

Simple Interest = $1932 (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 = 7% of Principal

= 7% of $4600

= ⁷/₁₀₀ × 4600

= ^{7 × 4600}/₁₀₀

= ³²²⁰⁰/₁₀₀ = 322

Thus, simple Interest for 1 year = $322

Now,

∵ If the simple Interest is $322, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₂₂ years

∴ If the simple Interest is $1932, then the time = ¹/₃₂₂ × 1932 years

= ^{1 × 1932}/₃₂₂ years

= ¹⁹³²/₃₂₂ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 10% simple interest?

(2) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $5822 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due if Christopher borrowed a sum of $4000 at 3% simple interest for 4 years.

(4) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $11780 to clear the loan, then find the time period of the loan.

(5) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $7668 to clear the loan, then find the time period of the loan.

(6) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $9176 to clear the loan, then find the time period of the loan.

(7) In how much time a principal of $3200 will amount to $3584 at a simple interest of 3% per annum?

(8) What amount will be due after 2 years if James borrowed a sum of $3000 at a 7% simple interest?

(9) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $9372 to clear the loan, then find the time period of the loan.

(10) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $7992 to clear the loan, then find the time period of the loan.