Question

You have an investment account that started with $3,000 10years ago and which now has grown to 11,000.

a. What annual rate of return have you earned? (you have made no additional contributions to the? account)?

b. If the investment account earns 13%per year from now? on, what will the? account's value be 10 years from? now?

2. You receive a 6,000 check from your grandparents for graduation. You decide to save it toward a down payment on a house. You invest it earning 10?% per year and you think you will need to have 12,000 saved for the down payment. How long will it be before the 6,000 has grown to12,000?

3. You are thinking of purchasing a house. The house costs $250,000.You have $36,000 in cash that you can use as a down payment on the? house, but you need to borrow the rest of the purchase price. The bank is offering a 30?-year mortgage that requires annual payments and has an interest rate of 8% per year. What will be your annual payment if you sign this? mortgage?

Answer 1

1.a. This question requires application of time value of money (TVM) concept. TVM concept is mathematically represented as:

FV = PV * (1 + r)ⁿ

where FV is the future value, PV is the present value, r is the rate of interest and n is the number of periods.

$11,000 = $3,000 * (1 + r)¹⁰

3.667 = (1 + r)¹⁰

r = 13.87%

b) Assuming you made $3,000 contribution with r = 13% for 10 years.

FV = $3,000 * (1 + 13%)¹⁰

FV = $10,183.7

2. This question would again need us to use the equation we used in last question.

$12,000 = $6,000 * (1 + 10%)ⁿ

2 = (1.10)ⁿ

Taking natural log at both sides of equation,

ln2 = n * ln(1.10)

n = ln 2/ln 1.1

n = 7.27 Years

3. This question specifically needs us to use the concept of annuities.

We need to calculate the per year payment that needs to be made to repay the 30 year loan.

Loan amount = $250,000 - $36,000 = $214,000 ---> PV of annuity of equal annual payments

PV of annuity is shown by mathematical relation:

Substituting values in equation above,

P = $19,009.07