1, Bob would like to have $26,000 in 5 years to use as a down payment on a house
ID: 2382768 • Letter: 1
Question
1, Bob would like to have $26,000 in 5 years to use as a down payment on a house. He plans on depositing an equal of money at the end of every month to save for this goal. If Bob can earn 6% interest per year(0.5% interest per month) what must he save per month to achieve this goal?
2. Sue has $24,000 to use as a down payment on a house and can afford to pay $800 per month for a mortgage. If the interest rate on a 15 year mortgage is 4.5% (this is an APR). What is the highest price house she can afford using a 15 year mortgage?
3, Larry would like to retire in 30 years. He estimates that he would need $2.1 million in order to retire. He is planning on depositing $1800 per month into his retirement account. What nominal interest rate would he need to earn in order to achieve his goal?
Explanation / Answer
Ans :
FV=A[ {(1+k)n -1}/k]
Where FV= Future value of annuity after n periods
A= periodic deposit
k= interest per period
n= duration of annuity
FV=26,000
k=0.5%
n=60
26,000= A[ {(1+.005)60- 1}/0.005
Or, 26,000= A[ {(1.35-1}/.005]
Or, 26,000 = 70A
Or A=371.43
Formula for finding present value of the mortgage
P = L[c(1 + c)n]/[(1 + c)n - 1]
Where P = monthly payment
L= total loan
C= monthly interest rate
N= no of months
Now P=800
N=180
C=4.5/12=0.375%
800= L [0.00375(1.00375)180]/[(1.00375)180-1]
Or , 800=L *0.0076
Or L = 800/0.0076=104,624
So the current value of the Mortgage loan is $104,624
Sue has $24,000 for down payment.
So Sue can afford a housing of value $128,624
FV=A[ {(1+k)n -1}/k]
Where FV= Future value of annuity after n periods =2,100,000
A= periodic deposit=$1800
k= interest per period=required
n= duration of annuity=360
so,
2,100,000= 1800[ {1+k)360-1}/k]
K=0.565 per month
=6.78% per annum
So require interest rate for Larr’s annuity is 6.78% per annum
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