Question

On 9/1/2019 you will start depositing $293 each month in an account that pays 5% rate of Interest. You will make a total number of 164 deposits. The present value of the annulty on 3/1/2019 Is $48,052 $34.763 $38,239 $48,345 $34,048
financial calculator steps please

Answer 1

Let’s first calculate the present value (PV) of deposits on 9/1/2019 in following manner –

Formula of the present value (PV) of annuity due (annuity due because deposits are made at the beginning of the period)

PV on 9/1/2019 = X * [1- (1+i) ^-n / i] * (1+i)

Where,

Present value (PV) on 9/1/2019 =?

Monthly deposits X = $293

And i= I/Y = 5% is the interest rate per annum or 5%/12 = 0.42% per month

Number of deposits n =164

Therefore,

PV on 9/1/2019 = $293 * [1- (1+0.42%) ^-164 / 0.42%] * (1+0.42%)

= $34,907.65

But we are required to calculate the present value of the annuity on 3/1/2009 or 6 months before 9/1/2019; therefore we have to discount above present value for 6 months

PV on 3/1/2019 = {PV on 9/1/2019} / (1+i) ^n

Where,

Present Value PV on 3/1/2019 =?

PV on 9/1/2019 = $34,907.65

And i= I/Y = 5% is the interest rate per annum or 5%/12 = 0.42% per month

Time period n = 6 months

Therefore,

PV on 3/1/2019 = $34,907.65/ (1+0.42%) ^6

= $34,047.54 or $34,048

Therefore correct answer is option: $34,048

For financial calculator to calculate PV –

Inputs are:

• N= 164
• I/Y = 0.0042
• PMT = 293