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Calculating Annuity Values. You want to have $60,000 in your savings account 12 years from now,...

Calculating Annuity Values. You want to have $60,000 in your savings account 12 years from now, and you’re prepared to make equal annual deposits into the account at the end of each year. If the account pays 6.4 percent interest, what amount must you deposit each year?
Calculating Annuity Values. Your company will generate $47,000 in annual revenue each year for the next seven years from a new information database. If the appropriate interest rate is 7.1 percent, what is the present value of the savings?

Expert Solution

Annuity -1 )We know the formula for future value of ordinary annuity as below

Future value of annuity is P*((1+r)ⁿ - 1)/r

Where P = Equalised periodic payment

r = rate of interest

n = Number of periods

Given the Futrure value is 60,000

Annual Interest rate is 6.4%

Number of years is 12

Now let us substitute this in the formula = 60,000 = P * ((1.064)¹²-1)/0.064

60,000 = P * (2.10523-1)/0.064

60,000 =P * 17.26922

P = 3474.39

Hence the annual deposits will be $3474.39

Annuity -2)Revenue generated by our company is in the form of annuity

Hence the formula for present value of annuity is

Present value of annuity - P*((1-(1+r)^-n)/r

Where P = Equalised periodic payment

r = rate of interest

n = Number of periods'

P = 47000

Interest rate is 7.1%

Number of periods is 7 years

Let the substitute this in the formula

Accordingly

Present value = 47000 * ( 1- (1.071)^-7)/(0.071)

47000 * (1-0.618691)/(0.071)

47000 * (0.381309)/0.071

= 252415.9

hence the present value will be 252415.9$

jeff jeffy answered 2 years ago

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