Simple Interest
Math MCQs

Question :  ( 1 of 10 )  Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $8320 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $5200

Rate of Simple Interest (R) = 10% per annum

Amount (A) = $8320

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 = $8320 – $5200 = $3120

Thus, Simple Interest = $3120

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 × 3120}/_{5200 × 10}

= ³¹²⁰⁰⁰/₅₂₀₀₀

= 6 years (using formula)

Thus, Time (T) = 6 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) = 10% per annum

Simple Interest = $3120 (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 = 10% of Principal

= 10% of $5200

= ¹⁰/₁₀₀ × 5200

= ^{10 × 5200}/₁₀₀

= ⁵²⁰⁰⁰/₁₀₀ = 520

Thus, simple Interest for 1 year = $520

Now,

∵ If the simple Interest is $520, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₂₀ years

∴ If the simple Interest is $3120, then the time = ¹/₅₂₀ × 3120 years

= ^{1 × 3120}/₅₂₀ years

= ³¹²⁰/₅₂₀ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 8% simple interest?

(2) If Sandra paid $4806 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(3) If Nancy paid $4980 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(4) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 5% simple interest?

(5) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $10320 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 5% simple interest.

(7) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 3% simple interest?

(8) Patricia had to pay $3339 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(9) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 9% simple interest.

(10) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 9% simple interest?