Question

Task 2 You decide to take out a mortgage of NOK 2,500,000. The maturity is set at 30 years and the interest rate is 1.98% per annum. The installment is to be paid monthly according to the annuity principle, and the first payment is in one month. a) What will be the forward amount? b) What is the residual loan right after payment number 60? You have also decided to star with individual retirement savings, and will save a fixed amount annually, for 20 years, in a high-interest account that guarantees 3% return per year. c) How much do you have to have in your account to be able to withdraw $ 50,000 every year for 10 years? The first withdrawal is one year after the last payment. d) How much do you need to save per year for the 20 years?

Answer 1

Part (A)

$F=P(\frac{F}{P},1.98\%,30)=2,500,000*1.8007=4,501,750\\$

$monthly\ interest\ rate=\frac{0.0198}{12}=0.00165\\ monthly\ installment=P(\frac{A}{P},0.165\%,360)=2,500,000*0.0036=9000$

Part (B)

9000, 0.165%, 300) residual loan after payment number 60 9000 * 236.4729 = 2, 128, 256.1

Part (C)

if a person starts saving today to withdraw $ 50000 per year for 10 years after 20 years

$amount\ needed\ now=50,000(\frac{P}{A},3\%,10)(\frac{P}{F},3\%,20)=50,000*8.530*0.5537=236,153.05\\$

Part (D)

amount to be saved each year for 20 years in order to withdraw $ 50,000 each year for 10 years

$A(\frac{F}{A},3\%,20)=50,000(\frac{P}{A},3\%,10)\\ 26.870*A=50,000*8.530\\ A=\frac{50,000*8.53}{26.87}=15,872.720$