Simple Interest
Math MCQs

Question :    Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $8008 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $5200

Rate of Simple Interest (R) = 6% per annum

Amount (A) = $8008

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 = $8008 – $5200 = $2808

Thus, Simple Interest = $2808

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 × 2808}/_{5200 × 6}

= ²⁸⁰⁸⁰⁰/₃₁₂₀₀

= 9 years (using formula)

Thus, Time (T) = 9 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) = 6% per annum

Simple Interest = $2808 (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 = 6% of Principal

= 6% of $5200

= ⁶/₁₀₀ × 5200

= ^{6 × 5200}/₁₀₀

= ³¹²⁰⁰/₁₀₀ = 312

Thus, simple Interest for 1 year = $312

Now,

∵ If the simple Interest is $312, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₁₂ years

∴ If the simple Interest is $2808, then the time = ¹/₃₁₂ × 2808 years

= ^{1 × 2808}/₃₁₂ years

= ²⁸⁰⁸/₃₁₂ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 8% simple interest?

(2) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 9% simple interest for 4 years.

(3) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 3% simple interest?

(4) If Charles borrowed $3900 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(5) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $7546 to clear the loan, then find the time period of the loan.

(6) David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $6816 to clear the loan, then find the time period of the loan.

(7) What amount does James have to pay after 5 years if he takes a loan of $3000 at 7% simple interest?

(8) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 9% simple interest.

(9) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8305 to clear it?

(10) Calculate the amount due if Linda borrowed a sum of $3350 at 4% simple interest for 4 years.