Simple Interest
Math MCQs

Question :    Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $8960 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $5600

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

Amount (A) = $8960

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 = $8960 – $5600 = $3360

Thus, Simple Interest = $3360

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 × 3360}/_{5600 × 6}

= ³³⁶⁰⁰⁰/₃₃₆₀₀

= 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) = $5600

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

Simple Interest = $3360 (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 $5600

= ⁶/₁₀₀ × 5600

= ^{6 × 5600}/₁₀₀

= ³³⁶⁰⁰/₁₀₀ = 336

Thus, simple Interest for 1 year = $336

Now,

∵ If the simple Interest is $336, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₃₆ years

∴ If the simple Interest is $3360, then the time = ¹/₃₃₆ × 3360 years

= ^{1 × 3360}/₃₃₆ years

= ³³⁶⁰/₃₃₆ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) Calculate the amount due if John borrowed a sum of $3200 at 3% simple interest for 3 years.

(2) Calculate the amount due if Sarah borrowed a sum of $3850 at 8% simple interest for 3 years.

(3) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $11584 to clear the loan, then find the time period of the loan.

(4) Find the amount to be paid if Linda borrowed a sum of $5350 at 8% simple interest for 7 years.

(5) How much loan did Jason borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9240 to clear it?

(6) If Richard paid $4176 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(7) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 7% simple interest?

(8) Calculate the amount due if David borrowed a sum of $3400 at 9% simple interest for 4 years.

(9) Find the amount to be paid if Linda borrowed a sum of $5350 at 10% simple interest for 8 years.

(10) Find the amount to be paid if Susan borrowed a sum of $5650 at 3% simple interest for 7 years.