Question

# Money is continuously deposited into an account at a rate of \$M per year.

Money is continuously deposited into an account at a rate of \$M per year.

Facts of the question:
Regular annual deposit of one million dollar.
Question doesnt mention the requirement, hence assuming that Future Value is required for annual deposits (Annuity) of one million dollar at a specific rate of interest.

I assume that interest rate is 3% per annum.
and period of investment assumed as 5 years

Formula for Future value of fixed annuity:
F = P * ([1 + I]^N - 1 )/I

P= Annual Deposits amount, in above case, its one million dollar

I=Interest rate, we assumed 3%

N= Number of payment, we assumed 5 years

Hence,
Future value (FV) = \$1Mn*([1+3%]^5-1)/3%
FV= \$1Mn*(1.03^5-1)/(3/100)

1.03^5 evaluates to 1.15927

1.03^5-1 evaluates to 0.159274

Multiply \$1Mn and 0.159274

\$1Mn*(1.03^5-1) evaluates to \$0.159274Mn

3/100 evaluates to

\$1Mn*(1.03^5-1)/(3/100) evaluates to \$5.30914Mn

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