Question

what is the future value in 2 years if you invest 150$ at the beginning of each month for 10 months starting today at a rate of 3% compounded quartely

Answer 1

A rate of 3 % compounded quarterly means an effective rate of 3/4% per quarter of 0.75% per quarter. There are 4 quarters in a year.

Monthly effective rate rate is as under

(1+monthly effective rate )^3 - 1 = Quarterly effective rate

(1+0.0075)^(1/3) - 1 = 0.00249378 or 0.249%

Thus, monthly effective rate is 0.249%.

Periods are all converted to months.

Required future value = 150*(1.00249^24) + 150*(1.00249^23) +... 150*(1.00249^15)

As this is in geometric progression, the above is equal to as under

150*(1.00249^24) * (1-1.00249^(-10)/ (1-1.00249^(-1))

= 159.2398*(9.8888) = $ 1574.69

Thus, future value at the end of two years is $1574.69.

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