Simple Interest
Math MCQs

Question :    Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $10064 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $6800

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

Amount (A) = $10064

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 = $10064 – $6800 = $3264

Thus, Simple Interest = $3264

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 × 3264}/_{6800 × 6}

= ³²⁶⁴⁰⁰/₄₀₈₀₀

= 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) = $6800

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

Simple Interest = $3264 (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 $6800

= ⁶/₁₀₀ × 6800

= ^{6 × 6800}/₁₀₀

= ⁴⁰⁸⁰⁰/₁₀₀ = 408

Thus, simple Interest for 1 year = $408

Now,

∵ If the simple Interest is $408, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₀₈ years

∴ If the simple Interest is $3264, then the time = ¹/₄₀₈ × 3264 years

= ^{1 × 3264}/₄₀₈ years

= ³²⁶⁴/₄₀₈ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) How much loan did Laura borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9027.5 to clear it?

(2) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $7680 to clear the loan, then find the time period of the loan.

(3) In how much time a principal of $3000 will amount to $3300 at a simple interest of 2% per annum?

(4) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 5% simple interest.

(5) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 5% simple interest?

(6) How much loan did Patricia borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6437.5 to clear it?

(7) How much loan did Steven borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7920 to clear it?

(8) Calculate the amount due if Robert borrowed a sum of $3100 at 3% simple interest for 3 years.

(9) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 4% simple interest?

(10) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 5% simple interest.