You have your choice of two investment accounts. Investment A is a 6-year annuity that features end-of-month $1,980 payments and has an interest rate of 7 percent compounded monthly. Investment B is an annually compounded lump-sum investment with an interest rate of 9 percent, also good for 6 years.
How much money would you need to invest in B today for it to be worth as much as Investment A 6 years from now? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer:

$112,166

Explanation:

the future value of Investment A:

payment = $1,980

n = 6 x 12 = 72

i = 9% / 12 = 0.75%

FVIFA = [(1 + i)ⁿ- 1 ] / i = [(1 + 0.0075)⁷² - 1 ] / 0.0075 = 95.007

future value = $1,980 x 95.007 = $188,114

now we need to determine the PV of investment B:

PV = $188,114 / (1 + 9%)⁶ = $112,166

Answer: $105,264.24

Explanation:

Step 1) Calculate Future Value of Investment A

Rate: .07/12 = .58%

Payment: $1,980

Term: 72 (6 years * 12 months)

Future Value: ?

In excel -> FV(.58,72,-1980,0)

Future Value = $176,538.67

Step 2) Calculate Present Value of Investment B using Investment A Future Value

Rate: .09

Payment: $0

Term: 6

Future Value: $176,538.67 (from step 1)

PV(.09,6,0,-176538.67)

Present Value = $105,264.24

Thats your answer!! ^^^^^

You can also use the formula or calculator, but I've found excel is the easiest/fastest.

Cheers!

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