1. For the last 15 years, Katarina has put $1,000 per month into an investment a
ID: 2802945 • Letter: 1
Question
1. For the last 15 years, Katarina has put $1,000 per month into an investment account at 4.75% per year compounded monthly. What is the present value of her account?
Katarina has decided to withdraw her entire investment account in 10 years through equal monthly withdrawals. How much will she receive each month?
At the same time she decided to start her withdrawal of her investment account, Katarina obtained a 20 year loan at 4.25% per year compounded monthly from the New Bank of Hilo to purchase her dream cabin on the slopes of Mauna Kea on the Big Island. Her monthly payment is exactly the same as the amount she will withdraw from her investment account each month. If she puts a down payment of $100,000, what was the price of the house?
Katarina decided to refinance her loan after 10 years. How much does she need to refinance?
Explanation / Answer
n = 15*12 = 180
r = 4.75% / 12 = 0.4%
Account balance = 1000*((1+0.4%)180 - 1) / 0.4% = 261781.07
Monthly withdrwal for next 10 years
n = 10*12 = 120
PMT = 261781.07*0.4% / (1 - (1+0.4%)-120) = 2744.72 per month
r = 4.25%/12 = 0.35%
n = 20*12 = 240
Original loan amount = 2744.72*(1- (1+0.35%)-240) / 0.35% = 443243.33
price of the house = 443243.33 + 100000 = 543243.33
n = 10*12 = 120
Amount to refinance = 2744.72*(1- (1+0.35%)-120) / 0.35% = 267940.41
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