In: Finance
Suzanne opens an account at a local bank on January 1, 2004 with a deposit of 4000 dollars. On October 1, 2004 she withdraws 1430 dollars. On April 1, 2005 she withdraws 850 dollars. And on April 1, 2007 she deposits 2090 dollars. Find the total present value of these transactions on July 1, 2006, if the account earns interest at a nominal rate of 7.6 percent convertible quarterly.
The solutions I've found on the website have not taken into account the future deposit and are incorrect, any suggestions?
Deposit 1 at 1st jan, 2004
Given : Amount = 4,000
Time till july 2006 = 2.5 years or 10 quaters
Rate of interest = 7.6% annual rate / 4 = 1.9% Quaterly
Value of deposit 1 at 1st july is calculated by using financial calculator
Inputs : pv = -4,000
Pmt = 0
I/y = 1.9%
N = 10
Fv = compute
We get, value of deposit 1 at 1st July as $4,828.38
Withdrawal at 1st October 2004
Given: amount = 1,430
Time till 1st july 2006 = 7 Quaters
Using financial calculator to calculate value at 1st july 2006
Inputs: Pv = -1,430
I/y = 7.6% / 4 = 1.9%
Pmt = 0
N = 7
Fv = compute
We get the value of withdrawal at 1st july 2006 as $1,631.38
Withdrawal at 1st April 2005
Given: value = $850
Time till 1st july= 5 quaters
Using financial calculator to calculate the value
Inputs: pv = -850
I/y = 1.9%
Pmt = 0
N = 5
Fv = compute
We get the value of withdrawal at 1st july 2006 as $933.88
Deposit at 1st April 2007
Given: Amount = 2,090
Time to 1st july 2006 = 3 quaters
In this case we use the financial calculator to calculate the present value of deposit as it is deposited after the time period at which the value is to be calculated.
Inputs: Fv = 2,090
Pmt = 0
I/y = 7.6% / 4 = 1.9%
N = 3
Pv = compute
We get the present value of deposit on 1st july 2006 as $1,975.26
The total present value on 1st July 2006 = present value of deposit in 2004 - present value of withdrawal
= 4,828.38 -1,631.38 - 933.88
= 2,263.12
We don't take into consideration the deposit of 2007 as the money was not in the account in 2006. So we cannot include the present value of last transaction.
If you need to include, then the present value of last transaction is also calculated above.