1. At the graduation party, your parents ask you about your plans for the future
ID: 2809207 • Letter: 1
Question
1. At the graduation party, your parents ask you about your plans for the future. You proudly tell them that you will earn enough at your new job to save up and purchase your first home. They are very happy to hear this news and ask you for a few more details. You explain your plan as follows: You plan to purchase a modest “starter” home for $156,000 in 6 years (i.e. at the end of the 6th year). You plan to save 20% of the purchase price for the down payment. To reach this goal you will make equal deposits into a savings account at the end of each month for the next six years.
a. If the savings account earns 6% compounded quarterly, how much will you need to deposit each month in order to save up enough for the down payment?
b. If your savings account instead earns 5.5% compounded daily, how much more/less (relative to the amount deposited in part a) would you need to deposit each month in order to reach your down payment goals?
2. Consider now that is the end of year 6 and you are ready to purchase you’re the new home discussed in question 1. The house costs $156,000 and you will have saved enough for a 20% down payment (i.e. you will have cash for this part of the purchase). You will finance the remaining cost of the house through a standard 30-year mortgage which has an APR of 6.25% compounded monthly.
a. If you accept these terms, how much will your equal monthly payment be each month?
b. Consider the 44 th payment. How much of your monthly payment will be applied to interest? How much will be applied toward principal?
c. After you have made the 120 th payment you are offered an opportunity to refinance your loan. Doing so would reduce your interest rate to 6% compounded monthly but allow you to repay the remaining money due over an additional 25 years. If you choose to do this, what would your new monthly payment be (i.e. how much will you pay)?
Explanation / Answer
down payment , D= 0.20* 156,000 = 31,200
time period of investment = t = 6 years
a) interest rate , i = 6% =0.06
interest rate per quarter , q = i/4 = 6/4 = 1.5% = 0.015
interest rate per month, r = q/3 = 1.5/3 = 0.5% = 0.005
no. of months , n = t*12 = 6*12 = 72
deposit each month = A
A*PVIFA( 0.5%, 72 ) = D
PVIFA(0.5%,72) =[ (1+r)n -1]/((1+r)n *r)
= [ (1.005)72 -1]/((1.0005)72 *0.005) = 60.33951394
A = D/PVIFA( 0.5%, 72 ) = 31200/60.33951394 = 517.0741 or 517.07 ( after rounding off to 2 decimal places)
deposit per month = 517.0741 or 517.07 ( after rounding off to 2 decimal places)
b)
interest rate , i = 5.5% =0.055
interest rate per day , q = i/365 = 5.5/365 = 0.015068% = 0.00015068
interest rate per month, r = q*30 = 0.015068*30 = 0.45205% = 0.0045205
no. of months , n = t*12 = 6*12 = 72
deposit each month = A
A*PVIFA( 0.45205%, 72 ) = D
PVIFA(0.45205%,72) =[ (1+r)n -1]/((1+r)n *r)
= [ (1.0045205)72 -1]/((1.0045205)72 *0.0045205) = 61.33980964
A = D/PVIFA(0.45205%,72) = 31200/ 61.33980964 = 508.6419 or 508.64 ( after rounding off to 2 decimal places)
deposit per month = 508.6419 or 508.64 ( after rounding off to 2 decimal places)
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