Question

1. You have $500,000 now and you believe you can earn 6.0% per year on your investment. How much will you have in 14 years?

2. You want to receive $85,000 per year forever. You believe that you can earn 6.00% on your money. How much would you need to invest today to achieve your goal?

3. Your Uncle Thomas put $25,000 into a college savings account for you 16 years ago. It is now worth $114,874 now. What is the approximate rate of return he earned on her account over that period?

4. You want to buy a car and find one that you really like. It’s a Tesla and it’s expensive! It costs $85,000. You have $12,000 as a down payment. The dealer is offering financing for 60 months with an APR of 4.00%. What is your monthly payment going to be? Please show your work.

Answer 1

Q-1)

Initial Investment = $500,00

Calculating the Future Value after 14 years:-

Where,

r = Interest rate = 6%

n= no of periods = 14 years

Future Value = $500,000*(1+0.06)^14

Future Value = $500,000*2.26090395575

Future Value =$1130,451.98

SO, amount you will have in 14 years is $1130,451.98

Q-2)

Cashflows to be received per year in perpetuity(or forever) = $85,000

Calculating the Present Value of Perpetuity:-

Present Value = Cashflows/Interest rate

= $85,000/6%

Present Value = $1,416,666.67

So, you need to invest today to achieve your goal is $1416,666.67

Q-3)

Initial amount invested 16 years ago = $25,000

Amount accumulated in Future value of $114,874

Calculating the approximate rate of return he earned on her account over that period:-

Where,

r = Interest rate

n= no of periods = 16 years

$114,874 = $25,000*(1+r)^16

4.59496 = (1+r)^16

Taking 16-root on both sides,

1.10 = (1+r)

r = 10%

So, the approximate rate of return he earned on her account over that period is 10%

Q-4)

Loan Amount = Car Price - Down Payment

= $85,000 - $12,000

= $73,000

Calculating the monthly Loan payment:-

Where, P = Loan amount = $73,000

r = Periodic Interest rate = 4%/12 = 0.3333%

n= no of periods = 60 months

Monthly Payment = $1344.41

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