Simple Interest
Math MCQs

Question :    David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $8256 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $4800

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

Amount (A) = $8256

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 = $8256 – $4800 = $3456

Thus, Simple Interest = $3456

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 × 3456}/_{4800 × 9}

= ³⁴⁵⁶⁰⁰/₄₃₂₀₀

= 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) = $4800

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

Simple Interest = $3456 (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 $4800

= ⁹/₁₀₀ × 4800

= ^{9 × 4800}/₁₀₀

= ⁴³²⁰⁰/₁₀₀ = 432

Thus, simple Interest for 1 year = $432

Now,

∵ If the simple Interest is $432, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₃₂ years

∴ If the simple Interest is $3456, then the time = ¹/₄₃₂ × 3456 years

= ^{1 × 3456}/₄₃₂ years

= ³⁴⁵⁶/₄₃₂ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) If Joshua paid $5684 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(2) If Paul paid $5264 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(3) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $8476 to clear the loan, then find the time period of the loan.

(4) 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.

(5) Find the amount to be paid if Jessica borrowed a sum of $5750 at 4% simple interest for 7 years.

(6) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 5% simple interest?

(7) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 3% simple interest?

(8) How much loan did Sarah borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6727.5 to clear it?

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

(10) Find the amount to be paid if James borrowed a sum of $5000 at 6% simple interest for 7 years.