You have your choice of two investment accounts. Investment A is a 14-year annui

Question

You have your choice of two investment accounts. Investment A is a 14-year annuity that features end-of-month $1,050 payments and has an interest rate of 6.6 percent compounded monthly. Investment B is a 6.1 percent continuously compounded lump sum investment, also good for 14 years. How much money would you need to invest in B today for it to be worth as much as investment A 14 years from now? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Explanation / Answer

Calculation of worth of investment A 14 years from now (Future value):

Future value of annuity = P *((1 +r)^n – 1))/ r

P = Monthly payment = 1050

r= Monthly rate = 6.6% /12 =   0.0055

n= number of months =14 years * 12 = 168

Hence,

Future value = 1050 *((1 +0.0055)^168 – 1))/ 0.0055

= 1050 *(2.512977434 – 1))/ 0.0055

= 1050 *275.0868062

= $288841.15

Calculation of lump sum investment in B today for it to be worth as much as investment A 14 years from now:

Present value = Future value / e^(r*t)

Future value   = $288841.15

e= 2.71828

r= rate of interest = 6.1% = 0.061

t= number of years = 14

Hence ,

Present value = 288841.15 / (2.71828^(0.061*14))

= 288841.15 / (2.71828^0.854)

= 288841.15 / 2.349022832

= $ 122962.26

Hence, $ 122962.26 lump sum investment should be made in investment B today for it to be worth as much as investment A 14 years from now.

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