Simple Interest
Math MCQs

Question :    Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $7912 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $4600

Rate of Simple Interest (R) = 9% per annum

Amount (A) = $7912

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 = $7912 – $4600 = $3312

Thus, Simple Interest = $3312

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 × 3312}/_{4600 × 9}

= ³³¹²⁰⁰/₄₁₄₀₀

= 8 years (using formula)

Thus, Time (T) = 8 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) = 9% per annum

Simple Interest = $3312 (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 = 9% of Principal

= 9% of $4600

= ⁹/₁₀₀ × 4600

= ^{9 × 4600}/₁₀₀

= ⁴¹⁴⁰⁰/₁₀₀ = 414

Thus, simple Interest for 1 year = $414

Now,

∵ If the simple Interest is $414, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₁₄ years

∴ If the simple Interest is $3312, then the time = ¹/₄₁₄ × 3312 years

= ^{1 × 3312}/₄₁₄ years

= ³³¹²/₄₁₄ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 3% simple interest.

(2) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 3% simple interest.

(3) Calculate the amount due if David borrowed a sum of $3400 at 9% simple interest for 3 years.

(4) Find the amount to be paid if Charles borrowed a sum of $5900 at 8% simple interest for 8 years.

(5) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 2% simple interest?

(6) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 3% simple interest.

(7) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 4% simple interest?

(8) What amount does William have to pay after 5 years if he takes a loan of $3500 at 8% simple interest?

(9) If Christopher borrowed $4000 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(10) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 6% simple interest.