Simple Interest
Math MCQs

Question :    David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $7152 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $4800

Rate of Simple Interest (R) = 7% per annum

Amount (A) = $7152

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 = $7152 – $4800 = $2352

Thus, Simple Interest = $2352

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 × 2352}/_{4800 × 7}

= ²³⁵²⁰⁰/₃₃₆₀₀

= 7 years (using formula)

Thus, Time (T) = 7 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) = $4800

Rate of Simple Interest (R) = 7% per annum

Simple Interest = $2352 (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 $4800

= ⁷/₁₀₀ × 4800

= ^{7 × 4800}/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 $2352, then the time = ¹/₃₃₆ × 2352 years

= ^{1 × 2352}/₃₃₆ years

= ²³⁵²/₃₃₆ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9142.5 to clear it?

(2) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 4% simple interest.

(3) Calculate the amount due if Jessica borrowed a sum of $3750 at 7% simple interest for 3 years.

(4) If Charles paid $4524 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(5) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 5% simple interest.

(6) What amount does James have to pay after 6 years if he takes a loan of $3000 at 2% simple interest?

(7) Calculate the amount due if John borrowed a sum of $3200 at 2% simple interest for 3 years.

(8) In how much time a principal of $3100 will amount to $3472 at a simple interest of 4% per annum?

(9) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $7544 to clear the loan, then find the time period of the loan.

(10) If Robert paid $3720 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.