You have the option of performing calculations manually BUT ARE STRONGLY ENCOURA
ID: 2620804 • Letter: Y
Question
You have the option of performing calculations manually BUT ARE STRONGLY ENCOURAGED to use a financial calculator or spreadsheet. Either way, you must specify what is being calculated to earn credit
1) You anticipate saving $1,800 a year for each of the next 25 years (NOT $1,800 once but $1,800 in each year) and anticipate earning 8% interest per year. Assuming annual compounding, how much do you expect to have in your account after 25 years?
2) You are borrowing $19,500 to buy a car. The terms of the loan call for monthly payments for 5 years at 5% percent interest. What is the amount of each monthly payment?
3)You borrow $320,000 to buy a house. 30-year mortgage rates are 4.25% and payments are made monthly. How much will be your mortgage payment be?
4) Referring back to question #19, how much total interest will you paying over the life of the mortgage?
Explanation / Answer
Question 1
We have
Future value of Annuity = A [((1+r)n-1) / r]
Where
A - Annuity payment (here 1,800)
r - rate per period (here 8%)
n - no. of periods (here 25)
Future value of Annuity = 1800 [(1.0825-1) / .08]
= 1800 [(6.8485-1) / .08]
= 1800* 73.1063
Future value of Annuity = $131,591.34
Question 2
We have
Present value of Annuity = A*[(1-(1+r)-n)/r]
Where
A - Annuity payment (?)
r - rate per period (here 5/12 =.42%)
n - no. of periods (here 60=5*12)
19,500 = A*[(1-1.0042-60)/.0042]
= A*[(1-0.7777)/.0042]
=A * 52.9286
A = 19,500 / 52.9286
Annuity payment = $368.42
Question 3
We have
Present value of Annuity = A*[(1-(1+r)-n)/r]
Where
A - Annuity payment (?)
r - rate per period (here 4.25/12 =.35%)
n - no. of periods (here 360=30*12)
320,000 = A*[(1-1.0035-360)/.0035]
= A*[(1-.2843)/.0035]
= A * 204.4857
A = 320,000 / 204.4857
= $1564.90
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