Question

Dorothy plans to invest some money so that she has $3,400 at the end of three years. Determine how much should she invest today given the following choices: (Do not round intermediate calculations and round your final answer to the nearest penny.)

a. 4.2 percent compounded daily.

Amount required to be invested

$

b. 4.9 percent compounded monthly.

Amount required to be invested

$

c. 5.2 percent compounded quarterly.

Amount required to be invested

$

d. 5.4 percent compounded annually.

Amount required to be invested

$

Answer 1

Let the amount invested today = P

Future Value required = F = $3400

Interest rate = r

Number of periods = n

Number of years = m = 3

Hence, F = P(1+r/n)^mn

Hence, P = F/(1+r/n)^mn

(a) r = 4.2% compounded daily

Hence, number of periods = n = 365

Hence, P = F/(1+r/n)^mn = 3400/(1+0.042/365)^3*365 = $2997.51

(b) r = 4.9% compounded monthly

Hence, number of periods = n = 12

Hence, P = F/(1+r/n)^mn = 3400/(1+0.049/12)^3*12 = $2936.08

(c) r = 5.2% compounded quarterly

Hence, number of periods = n = 4

Hence, P = F/(1+r/n)^mn = 3400/(1+0.052/4)^3*4 = $2911.83

(d) r = 5.4% compounded annually

Hence, number of periods = n = 1

Hence, P = F/(1+r/n)^mn = 3400/(1+0.054/1)^3*1 = $2903.74