Question

If $3,500 is invested at an interest rate of 6.25% per year compounded continuously, find the value of the investment after (a) 3 years, (b) 6 years, and (c) 9 years. (The formula can be found in the lecture notes or the textbook.)

Answer 1

(a) 3 years FV=$4,221.80

(b) 6 years FV=$5,092.46

(c) 9 years FV=$6,142.69

Explanation:

The formula for continuously compounded interest is

FV = PV x e^(i x t)

where,

FV=future value of the investment,

PV= present value,

i = stated interest rate,

t = time in years,

e= mathematical constant approximated as 2.7183.

In this case,

PV=$3,500

i = 6.25%

(a) 3 years

FV = PV x e^(i x t)

FV = $3,500 x e^(6.25%x3)

FV=$4,221.80

(b) 6 years

FV = $3,500 x e^(6.25%x6)

FV=$5,092.46

(c) 9 years

FV = $3,500 x e^(6.25%x9)

FV=$6,142.69