Derek will deposit $3,382.00 per year for 12.00 years into an account that earns 15.00%, The first deposit is made next year. He has $12,548.00 in his account today. How much will be in the account 37.00 years from today?

Total sum in the account = $5,438,822.55

Explanation:

Future Value of a single sum

The amount of $12,548 already in the account will earn interest for 37 years at the same rate of 15% compounded yearly. The amount this will accrue to is called the Future value of a lump sum. This can be worked as thus:

FV = PV * (1+r) ^ (n)

FV = 12,548 * (1.15) ^ (37)

= $12,548 * 176.124

= $2,210,011.85

Future Value of an annuity

The series of $3,382 to be invested per year to earn an interest of 12% per year for 12 years is called the annuity. The worth of this investment at the end of the 12th year is called the Future value of annuity. It can worked as out as follows:

FV = A * ((1+r) ^n - 1) / r

= 3,382 * ((1.15) ^ (12) - 1) / 0.15)

= 3,382 * 29.0016

= $98,083.64

From the 12th year to 37th year is another 25 years. So the $98,083.64 would be treated as another lump sum invested. So we work out its future value as follows:

FV = 98,083.64 * (1.15) ^ (25)

= 98,083.64 * 32.9189

=$ 3,228,810.70

Total sum in the account at the end of the 37th year:

= $2,210,011.85 + $ 3,228,810.70

= $5,438,822.55