Question

In: Finance

August Street, Inc. wants to have $7,500,000 in an account exactly 16 years from today. They...

  1. August Street, Inc. wants to have $7,500,000 in an account exactly 16 years from today. They will make equal quarterly payments of $50,000 beginning next quarter and ending in 16 years. The account earns 8.00% p.a., compounded quarterly. August Street must have $_______ in its account today.

Solutions

Expert Solution

Future value = $ 7500000

No.of Years = 16

Rate of interest = 8% p.a Compounded Quarterly.

Rate of interest per Quarter = 8% /4 = 2% per Quarter.

Quarterly Payment = $ 50,000

We know that

Present value of $ 75,00000 = Present value of the amount exist as on today + Present value of Quarterly payments of $ 50,000 made during the 16 years

Step 1: Computation of Present value of $ 75,00000

Future Value = Present value ( 1+i/4)^4n( Interest compounded Quarterly)

i= Rate of interest and n = No.of Years

$ 75,00000 = Present value( 1+8/400)^4*16

$ 75,00000 = Present value( 1+0.02)^64

$ 75,00000 = Present value ( 1.02)^64

$ 75,00000 = Present value * 3.5515

$ 7500000/3.5515 = Present value

Present value = $ 21,11788

Hence the Present value of $ 7500000 = $ 21,11788

Step 2: Computation of Present value of Quartely Payments of $ 50,000 made during 16 years

We know that Present value of the Ordinary Annuity = C [ { 1-( 1+i)^-n}/i]

Here C = Cash flow per period

i= Interest

n = Number of Payments

Number of payments in 16 years = 16*4 = 64 Payments

Present value of Ordinary Annuity = $ 50,000[ { 1-( 1+0.02)^-64 }/0.02]

= $ 50,000[ { 1-( 1.02)^-64}/0.02]

= $ 50,000[{ 1- 1/( 1.02)^64}/0.02]

= $ 50000[ { 1-0.2816}/0.02]

= $ 50000[ 0.7814/0.02]

= $ 50,000[ 35.92141]

= $1796071.743

Step 3: Computation of Present value of the amount exist as on today

We know that

Present value of $ 75,00000 = Present value of the amount exist as on today + Present value of Quarterly payments of $ 50,000 made during the 16 years

$ 21,11788 = Present value of the amount exist as on today + $ 1796072

$ 21,11788-$ 1796072 = Present value of the amount exist as on today.

$ 315716 = Present value of the amount exist as on today.

Hence August street must have $ 315716 in its account today.

If you are having any doubts,please post a comment.

Thank you. Please rate it.


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