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You invest $500 in a mutual fund at the end of each month from 2019 to...

You invest $500 in a mutual fund at the end of each month from 2019 to 2043, inclusive. You stop investing after January 1, 2044 and the blance in the account continues to accumulate. What is the account balance on December 31, 2050 if the nominal annual rate is 10% compounded monthly

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Answer #1

Monthly deposit = $500
Number of deposits = 300 (25 years * 12)
Annual interest rate = 10%
Monthly interest rate = 0.8333%

Accumulated sum on December 31, 2050 = $500*1.008333^383 + $500*1.008333^382 + … + $500*1.008333^85 + $500*1.008333^84
Accumulated sum on December 31, 2050 = $500 * 1.008333^84 * (1.008333^300 - 1) / 0.008333
Accumulated sum on December 31, 2050 = $500 * 2,663.920017
Accumulated sum on December 31, 2050 = $1,331,960.01

So, accumulated account balance on December 31, 2050 is $1,331,960.01 or $1,331,960

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