Simple Interest
Math MCQs

Question :    David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $7824 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $4800

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

Amount (A) = $7824

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 = $7824 – $4800 = $3024

Thus, Simple Interest = $3024

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 × 3024}/_{4800 × 7}

= ³⁰²⁴⁰⁰/₃₃₆₀₀

= 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) = $4800

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

Simple Interest = $3024 (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 $4800

= ⁷/₁₀₀ × 4800

= ^{7 × 4800}/₁₀₀

= ³³⁶⁰⁰/₁₀₀ = 336

Thus, simple Interest for 1 year = $336

Now,

∵ If the simple Interest is $336, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₃₆ years

∴ If the simple Interest is $3024, then the time = ¹/₃₃₆ × 3024 years

= ^{1 × 3024}/₃₃₆ years

= ³⁰²⁴/₃₃₆ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 6% simple interest?

(2) Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $9128 to clear the loan, then find the time period of the loan.

(3) What amount does William have to pay after 5 years if he takes a loan of $3500 at 8% simple interest?

(4) Calculate the amount due if Richard borrowed a sum of $3600 at 4% simple interest for 3 years.

(5) Find the amount to be paid if Sarah borrowed a sum of $5850 at 7% simple interest for 7 years.

(6) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 2% simple interest.

(7) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $5964 to clear the loan, then find the time period of the loan.

(8) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 10% simple interest?

(9) What amount will be due after 2 years if James borrowed a sum of $3000 at a 5% simple interest?

(10) 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?