In: Finance
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.
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