Question

Find the future value of an investment of $2,900 made today for the following rates and periods: (If you solve this problem with algebra round intermediate calculations to 4 decimal places, in all cases round your answers to the nearest penny.)

Excel Template
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a. 6.25 percent compounded semiannually for 12 years.

Future value

$

b. 7.63 percent compounded quarterly for 6 years.

Future value

$

c. 8.9 percent compounded monthly for 10 years.

Future value

$

d. 10 percent compounded daily for 3 years.

Future value

$

e. 8 percent compounded continuously for 2 years.

Future value

$

Answer 1

Given investment = $2900

Future value = present value * (1 + r/n)^nt

n = number of times compounded

t= time period

r= interest rate

a.

6.25 percent compounded semiannually for 12 years.

For semi annually n= 2

Future value = 2900 * (1+ 0.0625/2)^ 2*12 = 2900 * 1.03125^24 = 2900 * 2.092835422 = $6069.2227

b.

7.63 percent compounded quarterly for 6 years.

For quarterly n=4

Future value = 2900 * (1+ 0.0763/4)^ 4*6 = 2900 * 1.019075^24 = 2900 * 1.573792756 = $4563.9989

c.

8.9 percent compounded monthly for 10 years.

For quarterly n=12

Future value = 2900 * (1+ 0.089/12)^ 12*10= 2900 * 1.007416667^120 = 2900 * 2.427145345 = $7038.7215

d.

10 percent compounded daily for 3 years.

For quarterly n=365

Future value = 2900 * (1+ 0.1/365)^ 365*3= 2900 * 1.000273973^1095 = 2900 * 1.349803345 = $3914.4297

e.

8 percent compounded continuously for 2 years.

Future value = Present value * e^rt

Future value = 2900 * e^0.08*2 = 2900 * e^0.16 = 2900 * 1.173510871 = $3403.1815