I have some math problems in Finance 1000, Plz help me, thank you !! 1. abby won
ID: 2637444 • Letter: I
Question
I have some math problems in Finance 1000, Plz help me, thank you !!
1. abby won $11500 in the lottery. she wants to use some of the winings as a down payment for a home. she will be ready to purchase a home in 10 years. how much of her winnings should she deposit today at 6.2% interest, compounded monthly to ensure that she has $20000 when she is ready to buy a home?
2.casey can spend $350 a month on a car payment. the dealer will give him $5000 for the trade in value of his current car. the credit union is offering him a car loan at 4% for three years. how much can casey spend on a new car?
3. charlie wants to retire in 25 years. he rencently changed jobs and started saving in a new retirement plan. he rolled over his IRA from the previous job with a balance of $17000 into an account that earns an average of 8% annually. he begins a new 401K account deposing $250 monthly into the account , which earns 9% compunded monthly. how much will have in the IRA account in 25 years?
4. using the information in the previous question about charlie's two retirement account, calculate how much money he will have for retirement in 25 years.
Explanation / Answer
Answer to point no:1
Amount at the end of 10 years needs to be $20,000.
Interest rate = 6.2%
Frequency of interest calculation is monthly. Number of interest periods with in 10 years is 12*10=120
Using the undermentioned formula, assuming that P is the principal amount that needs to be deposited today to derive $20,000 at the end of 10 years.
A= P(1+r/100)^n
A is the amount at the time of maturity, in this case it is $20,000
P is the principal amount, this needs to be found
r= rate of interest, in this case it is 6.2% and per month interest rate is 6.2%/12 =0.5167
n is the frequency of compouding interest, in this case it is 120.
Applying the values in the formula
$20,000 = P + (1+.5167/100)^120
$20,000= P+(100.5167/100)^120
$20,000=P+1.85596
P= $20000/1.85596
P= 10.776.08
So, $10,776.08 needs to be deposited from the lottery amount inorder to arrive at $20,000 at the end of 10 years.
Answer for Point no:2
To manually calculate EMI the formula is EMI=Principal amount[rate of interest]/[1-(1+rate of interest)^ -n]
Rate of interest is 4% as the interest is calculated monthly, monthly effective rate of interest is .0033%
EMI here is 350
n= 36 as the tenure is 3 years
by substituting these values in the above said formula Principal amount is arrived.
350=Principal amount* [.0033/{1-(1+.0033)^ -36}]
350=Principal amount*0.02952
Principal amount = 350/0.02952
Principal amount = $11,854.7 rounded to 11855
As Casey is already having $5,000 from the sale of his car. Maximum amount he can afford to buy a car is $11,855+$5,000= $16, 855.
Answer for Point no:3
Earnings from 404K account after 25 years:
Formula to calculate maturity value of recurring deposit is
Maturity amount= R[(1+i)^n-1]/i
R=monthly deposited amount, here it is $250
i is the interest rate as it is monthly compounding in this case it is =9/1200 =0.0075
substituting the values in the formula Maturity amount is arrived as below:
M= 250[(1+.0075)^300-1]/.0075)
M= 250*8.408/.0075
M=$280,280.48
There fore he will have $280, 280 in the IRA account at the end of 25 years.
Answer for point no:4
Principal amount is $17,000
Rate of interest is 8%
Number of times the interest is compunded in the period of 25 years is 25 as it is yearly compounding.
So, applying the values into the formula A= P(1+r/100)^n
A= $17,000(1+8/100)^25
A=$116,424
So, the total amount at the end of 25 years is $116,424+$280,280.48 = $396,704.48