Question

What is the value today of a money machine that will pay $2,848.00 every six months for 16.00 years? Assume the first payment is made 3.00 years from today and the interest rate is 14.00%.

Answer format: Currency: Round to: 2 decimal places.

Derek will deposit $865.00 per year into an account starting today and ending in year 6.00. The account that earns 9.00%. How much will be in the account 6.0 years from today?

Answer format: Currency: Round to: 2 decimal places

could really use the help. not sure if I'm doing the process right. thanks

Answer 1

What is the value today of a money machine that will pay $2,848.00 every six months for 16.00 years? Assume the first payment is made 3.00 years from today and the interest rate is 14.00%.

The present value of payments can be calculated in following manner

PV = PMT * [1-(1+i) ^-n)]/i

Where,

Present value (PV) =?

PMT = six-monthly payments = $2,848.00

n = N = number of payment = 2 *16 years = 32 six-monthly payments

i = I/Y = interest rate per year = 15 %; therefore six-monthly interest rate= 14%/2 = 7%

Therefore,

PV = $2,848.00 * [1- (1+7%) ^-32]/7%

= $36,017.39

But this present value is after 3 years as the payment starts after 3 years

Therefore Present value today = present value is after 3 years / (1+i) ^ (3*2)

= $36,017.39 / (1+7%) ^6

= $23,999.91

Derek will deposit $865.00 per year into an account starting today and ending in year 6.00. The account that earns 9.00%. How much will be in the account 6.0 years from today?

We can calculate the Future value (FV) of these annual deposits by using interest rate of 9% (Future value of annuity due formula as the deposits are at the beginning of each year)

FV = PMT*(1+i) *{(1+i) ^n−1} / i

Where FV =?

PMT = Annual deposit = $865.00

n = N = number of payments = 6 (year)

i = I/Y = interest rate per year = 9%

Therefore,

FV = $865.00*(1+9%) *{(1+9%) ^6−1} / 9%

FV = $7,093.38

Therefore Derek will have $7,093.38 in his account after 6 years.