Question

For 2 years, you deposit $45 per month in an account that earns 10% annually with monthly compounding. After the first five months, you deposit a $500 lump sum. Six months after that (on month 11), you deposit $1000 into your account. Eight months later (on month 19), you make a $750 deposit. You then move your money to an account that has 3.5% monthly interest compounded weekly. You keep it in this account for 3 years. After this time period, what is the amount of money you have saved (assume 4 weeks in 1 month)? $12871.79

Answer 1

We need to calculate the FW of the cash flow here. There are three separate cash flow in the first part.
FW = PMT * (1+Interest Rate)Duration

$45 deposited in each month for 2 years or 24 months.
Interest rate is 10% per year compounded monthly.
FW = 45 * FVIFA
45 * 26.4469 = 1190.11
OR
=FV(10%/12,24,-45)
= 1190.11

$500 deposited in the 5th month so it will have duration of 19 months
500 * 1.1708 = 585.39
or
=FV(10%/12,19,,-500)
= 585.39

Similarly, $1000 deposited in the 11th month
=FV(10%/12,13,,-1000)
= 1113.92

$750 in the 19th month
=FV(10%/12,5,,-750)
= 781.78

The FW at the end of 24 months
1190.11 + 585.39 + 1113.92 + 781.78 = 3671.20

This amount has earned 3.5% monthly interest compounded weekly.
Duration = 3 years or 156 weeks

3671.20 * (1+(0.035/4))^156
= 3671.20 * (1+0.00875)^156
= 14290.30