Final answer:
To calculate the total amount in Gabe's RRSP account by July 1, 2016, the future values of all three separately timed deposits are computed considering their individual compounding periods. The amount is the sum of the future values of these deposits.
Step-by-step explanation:
To find the amount in Gabe's RRSP account on July 1, 2016, we need to calculate the future value of each deposit separately, as they are made at different times and will earn interest for different durations. The account earns 7.8% interest per annum compounded monthly.
First, we calculate the future value of the initial $1000 deposit made on December 1, 2008. This deposit has been in the account for 7 years and 7 months (91 months) by July 1, 2016. We use the formula for compound interest:
FV = P × (1 + r/n)^(nt)
Where FV is the future value, P is the principal amount, r is the annual interest rate (in decimal), n is the number of times the interest is compounded per year, and t is the time in years. For monthly compounding, n=12.
Do the same for the next two deposits; the second $1000 has been in for 6 years and 6 months (78 months), and the third $1000 for 4 years and 3 months (51 months).
Add the future values of all three deposits to get the total amount in the account on July 1, 2016.