Question

You've graduated from college and have wisely started saving for retirement immediately. However, you don't save much and only invest $200 per year in the stock market. Your portfolio earns a 9% annual return, how many years will it take you to accumulate $12,000 in the account?

Suppose you bought a house on January 1 and took out a mortgage for $400,000. The amortized loan requires annual payments for 15 years. For tax purposes you want to figure out how much you will pay in interest in each year of the loan. Assuming the loan's interest rate is 9%, how much will you pay in interest in the 2nd year of the loan.

Answer 1

You've graduated from college and have wisely started saving for retirement immediately. However, you don't save much and only invest $200 per year in the stock market. Your portfolio earns a 9% annual return, how many years will it take you to accumulate $12,000 in the account?

We can use following formula to calculate the Future value annual savings

FV = PMT * [(1+i) ^n – 1] /i

Where FV = future value of annual savings =$12,000

PMT or saving per year = $200 per annum

And i= I/Y = 9% is annual interest rate

The time period n =?

Therefore,

$12,000 = $200 * [(1+9%) ^n -1]/ 9%

Or n = 21.54 years

Therefore it will take 21.54 years to save $12,000.

Suppose you bought a house on January 1 and took out a mortgage for $400,000. The amortized loan requires annual payments for 15 years. For tax purposes you want to figure out how much you will pay in interest in each year of the loan. Assuming the loan's interest rate is 9%, how much will you pay in interest in the 2nd year of the loan.

We can use PV of an Annuity formula to calculate the annual payment of loan

PV = PMT * [1-(1+i) ^-n)]/i

Where PV = $400,000

PMT = Annual payment =?

n = N = number of payments = 15 years

i = I/Y = interest rate per year = 9%

Therefore,

$400,000 = PMT* [1- (1+9%) ^-15]/9%

PMT = $49,623.55

Annual payment is $49,623.55

Let’s calculate Outstanding balance on loan after 1 year of loan; it can be calculated by assuming PMT = Annual payment = $49,623.55

n = N = number of payments = 14 years

Therefore,

Outstanding balance on loan after one year (PV1) = $49,623.55 * [1- (1+9%) ^-14]/9%

= $386,376.45

And Outstanding balance on loan after 2 year of loan; it can be calculated by assuming PMT = Annual payment $49,623.55

n = N = number of payments = 13 years

Therefore,

Outstanding balance on loan after two years (PV2) = $49,623.55 * [1- (1+9%) ^-13]/9%

= $371,526.77

Now the interest will be paid in only the second year = Annual payment of second year – (Outstanding balance on loan after one year (PV1) - Outstanding balance on loan after two years (PV2))

= $49,623.55 – ($386,376.45 - $371,526.77)

= $49,623.55 - $14,849.67

= $34,773.88

Interest paid in the 2nd year of the loan is $34,773.88