Question

Suppose ​$29,000 is invested at an annual rate of 5​% for 20 years. Find the future value if interest is compounded as follows.

a. Annually

b. Quarterly

c. Monthly

d. Daily​ (365 days)

e. Continuously

a. Compounded​ annually, the future value is __________________________________

​(Do not round until the final answer. Then round to the nearest cent as​ needed.)

b. Compounded​ quarterly, the future value is _____________.

​(Do not round until the final answer. Then round to the nearest cent as​ needed.)

c. Compounded​ monthly, the future value is ______________

​(Do not round until the final answer. Then round to the nearest cent as​ needed.)

d. Compounded​ daily, the future value is ________________

​(Do not round until the final answer. Then round to the nearest cent as​ needed.)

e. Compounded​ continuously, the future value is ____________

​(Do not round until the final answer. Then round to the nearest cent as​ needed.)

Answer 1

PV = $29000

Annual rate r = 5%

time period, t = 20 year

a). For compounded annually, compounding frequency n = 1

Future value is calculated using formula,

FV = PV*(1+r/n)^(n*t) = 29000*(1+0.05/1)^(1*20) = $76945.63

b). For compounded quarterly, compounding frequency n = 4

Future value is calculated using formula,

FV = PV*(1+r/n)^(n*t) = 29000*(1+0.05/4)^(4*20) = $78343.06

c). For compounded monthly, compounding frequency n = 12

Future value is calculated using formula,

FV = PV*(1+r/n)^(n*t) = 29000*(1+0.05/12)^(12*20) = $78666.57

d). For compounded daily, compounding frequency n = 365

Future value is calculated using formula,

FV = PV*(1+r/n)^(n*t) = 29000*(1+0.05/365)^(365*20) = $78824.77

e). For compounded continuously,

Future value is calculated using formula,

FV = PV*e^(r*t) = 29000*e^(0.05*20) = $78830.17