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 does Sarah have to pay after 6 years if he takes a loan of $3850 at 5% simple interest?

(2) Calculate the amount due if Susan borrowed a sum of $3650 at 6% simple interest for 3 years.

(3) What amount does James have to pay after 5 years if he takes a loan of $3000 at 5% simple interest?

(4) Find the amount to be paid if Barbara borrowed a sum of $5550 at 6% simple interest for 7 years.

(5) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $5964 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 6% simple interest.

(7) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $7020 to clear the loan, then find the time period of the loan.

(8) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $11020 to clear the loan, then find the time period of the loan.

(9) If Susan borrowed $3650 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(10) Find the amount to be paid if Thomas borrowed a sum of $5800 at 9% simple interest for 8 years.