Simple Interest
MCQs Math

Question:     Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $8320 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution And Explanation

Solution

Given,

Principal (P) = $5200

Rate of Simple Interest (R) = 6% per annum

Amount (A) = $8320

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 = $8320 – $5200 = $3120

Thus, Simple Interest = $3120

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 × 3120}/_{5200 × 6}

= ³¹²⁰⁰⁰/₃₁₂₀₀

= 10 years (using formula)

Thus, Time (T) = 10 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) = $5200

Rate of Simple Interest (R) = 6% per annum

Simple Interest = $3120 (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 = 6% of Principal

= 6% of $5200

= ⁶/₁₀₀ × 5200

= ^{6 × 5200}/₁₀₀

= ³¹²⁰⁰/₁₀₀ = 312

Thus, simple Interest for 1 year = $312

Now,

∵ If the simple Interest is $312, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₁₂ years

∴ If the simple Interest is $3120, then the time = ¹/₃₁₂ × 3120 years

= ^{1 × 3120}/₃₁₂ years

= ³¹²⁰/₃₁₂ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) If Sarah borrowed $3850 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(2) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 3% simple interest.

(3) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $8000 to clear the loan, then find the time period of the loan.

(4) Find the amount to be paid if Thomas borrowed a sum of $5800 at 10% simple interest for 7 years.

(5) Calculate the amount due if William borrowed a sum of $3500 at 4% simple interest for 3 years.

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

(7) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $6468 to clear the loan, then find the time period of the loan.

(8) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 2% simple interest?

(9) In how much time a principal of $3100 will amount to $3596 at a simple interest of 4% per annum?

(10) Calculate the amount due if Susan borrowed a sum of $3650 at 3% simple interest for 4 years.