Question

Find the future value of an investment of $3,100 made today for the following rates and periods:

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

Present value of investment = $3,100

a.

Investment period, t = 12 years

Interest rate, r = 6.25%

Compounding frequency, n = 2 (sem-annually)

Future value of investment = Present value of investment *(1+r/n)^nt = 3100*(1+6.25%/2)^2*12 = 3100*2.092835

= $6,487.79

b.

Investment period, t = 6 years

Interest rate, r = 7.63%

Compounding frequency, n = 4 (quarterly)

Future value of investment = Present value of investment *(1+r/n)^nt = 3100*(1+7.63%/4)^4*6 = 3100*1.573793

= $4,878.76

c.

Investment period, t = 10 years

Interest rate, r = 8.90%

Compounding frequency, n = 12 (monthly)

Future value of investment = Present value of investment *(1+r/n)^nt = 3100*(1+8.9%/12)^12*10 = 3100*2.427145

= $7,524.15

d.

Investment period, t = 3 years

Interest rate, r = 10%

Compounding frequency, n = 365 (daily)

Future value of investment = Present value of investment *(1+r/n)^nt = 3100*(1+10%/365)^365*3 = 3100*1.349803

= $4,184.39

e.

Investment period, t = 2 years

Interest rate, r = 8%

For continuous compounding,

Future value of investment = Present value of investment *e^rt = 3100 *e^8%*2 = 3100*1.173511

= $3,637.88