Simple Interest
Math MCQs

Question :    Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $9360 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $5200

Rate of Simple Interest (R) = 8% per annum

Amount (A) = $9360

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 = $9360 – $5200 = $4160

Thus, Simple Interest = $4160

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 × 4160}/_{5200 × 8}

= ⁴¹⁶⁰⁰⁰/₄₁₆₀₀

= 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) = 8% per annum

Simple Interest = $4160 (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 = 8% of Principal

= 8% of $5200

= ⁸/₁₀₀ × 5200

= ^{8 × 5200}/₁₀₀

= ⁴¹⁶⁰⁰/₁₀₀ = 416

Thus, simple Interest for 1 year = $416

Now,

∵ If the simple Interest is $416, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₁₆ years

∴ If the simple Interest is $4160, then the time = ¹/₄₁₆ × 4160 years

= ^{1 × 4160}/₄₁₆ years

= ⁴¹⁶⁰/₄₁₆ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $9350 to clear the loan, then find the time period of the loan.

(2) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 2% simple interest?

(3) Find the amount to be paid if Christopher borrowed a sum of $6000 at 6% simple interest for 8 years.

(4) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $9804 to clear the loan, then find the time period of the loan.

(5) Find the amount to be paid if Mary borrowed a sum of $5050 at 2% simple interest for 8 years.

(6) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 3% simple interest?

(7) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $12000 to clear the loan, then find the time period of the loan.

(8) Find the amount to be paid if Richard borrowed a sum of $5600 at 8% simple interest for 7 years.

(9) 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?

(10) Calculate the amount due if Charles borrowed a sum of $3900 at 6% simple interest for 3 years.