Simple Interest
Math MCQs

Question :    Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $8112 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $5200

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

Amount (A) = $8112

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 = $8112 – $5200 = $2912

Thus, Simple Interest = $2912

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 × 2912}/_{5200 × 7}

= ²⁹¹²⁰⁰/₃₆₄₀₀

= 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) = $5200

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

Simple Interest = $2912 (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 $5200

= ⁷/₁₀₀ × 5200

= ^{7 × 5200}/₁₀₀

= ³⁶⁴⁰⁰/₁₀₀ = 364

Thus, simple Interest for 1 year = $364

Now,

∵ If the simple Interest is $364, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₆₄ years

∴ If the simple Interest is $2912, then the time = ¹/₃₆₄ × 2912 years

= ^{1 × 2912}/₃₆₄ years

= ²⁹¹²/₃₆₄ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 9% simple interest?

(2) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 4% simple interest.

(3) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $10070 to clear the loan, then find the time period of the loan.

(4) How much loan did Michael borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6625 to clear it?

(5) Find the amount to be paid if Robert borrowed a sum of $5100 at 6% simple interest for 7 years.

(6) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 3% simple interest.

(7) If James paid $3360 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(8) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 7% simple interest?

(9) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $11020 to clear the loan, then find the time period of the loan.

(10) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $7052 to clear the loan, then find the time period of the loan.