Question

Calvin Jones is creating a college investment fund for his daughter. He will put in 1000 at the beginning of each year for the next 15 years. if he earns 6% (compounded quarterly ) on this investment, how much will he have in exactly 15 years.

Answer 1

$1000 is being invested at the beginning of each year. So, it is annuity due. In annuity due, payments/ investments are made at the beginning of each period.

Rate of interest is 6% compounded quarterly. So, quarterly rate is 6% / 4 = 1.5%

Now the formula for future value for annuity due is:

FV = (1+r) * P * ((1+r)ⁿ - 1 ) / r

where, FV= Future value , r = rate of interest = 1.5% , P = Periodic payment, n = time period = 15 * 4 = 60

Now, putting the values in the above formula we get,

FV = (1+ 1.5%) * $1000 * ((1+1.5%)⁶⁰ - 1 ) / 1.5%

FV = (1+ 0.015) * $1000 * ((1+0.015)⁶⁰ - 1 ) / 0.015

FV = (1.015) * $1000 * ((1.015)⁶⁰ - 1 ) / 0.015

FV = (1.015) * $1000 * ((2.44321977569 - 1 ) / 0.015

FV = (1.015) * $1000 * (1.44321977569) / 0.015

FV = (1.015) * $1000 * 96.2146517126

FV = (1.015) * 96214.6517126

FV = 97657.8714883, which is the required amount after 15 years.