You have your choice of two investment accounts. Investment A is a 12-year annui

Question

You have your choice of two investment accounts. Investment A is a 12-year annuity that features end-of-month $1,900 payments and has an interest rate of 8.3 percent compounded monthly. Investment B is a 7.8 percent continuously compounded lump sum investment, also good for 12 years.

How much money would you need to invest in B today for it to be worth as much as Investment A 12 years from now?

You have your choice of two investment accounts. Investment A is a 12-year annuity that features end-of-month $1,900 payments and has an interest rate of 8.3 percent compounded monthly. Investment B is a 7.8 percent continuously compounded lump sum investment, also good for 12 years.

Explanation / Answer

Investment A

Monthly Investment =$1900

n(period) = 144 payments

Interest =8.3 % compunded monthly

Future value of Investment A =$469709.94

Investment B

So we need to pay a lump sum investment to get Future value of investment of B as $469710.

A = Pert, whre A is Future value, P is the Principal, r is the interest rate and t is time

469710 = Pe0.0780*12

P = 469710/e0.936

P= 469710/2.54796

P= 184217.20

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