Question

1. Heather lends a friend $18,000 for which her friend will repay him $36,000 at the end of 11 years. What interest rate is Heather charging her friend? (Round to 2 decimal places)

2. What is the present value of an annuity of $140 received at the end of each year for 12 years? Assume a discount rate of 8%. The first payment will be received one year from today (round to nearest dollar).

3. You decide you want your child to be a millionaire. You have a daughter today and you deposit $59,000 in an investment account that earns 7.5% per year. The money in the account will be distributed to your daughter whenever the total reaches $3,750,000. How old will your daughter be when she gets the money (rounded to the nearest year)?

4. An investment is expected to yield $700 in three years, $800 in five years, and $900 in seven years. What is the present value of this investment if our opportunity rate is 6%?

5. Molly would like to know the monthly payment on the following two loans:

a) $44,000, 3.9% interest rate, 96 months

b) $44,000, 3.9% interest rate, 60 months

Please show your work

Answer 1

1) Present Value (PV) = $18,000

Future Value (FV) = $36,000

Time (n) = 11 years

Interest rate (r) = ?

Future Value = Present Value (1 + r)ⁿ

36,000 = 18,000 (1 + r)¹¹

2 = (1 + r)¹¹

$\sqrt[11]{2}$ = (1 + r)

1.06504 = 1 + r

r = 0.06504 * 100

r = 6.50%

[NOTE; We can calculate the interest rate by using rule of 72 also as the future value is becoming double the present value. The interest rate will be (72/Years) = 72 / 11 = 6.55% . As we can see that here the interest rate is slightly changed the actual rate . There will be little more value using this interest rate . But actual rate of 6.50% will give us the actual double value after 11 years.]

{NOTE : As per Chegg guidelines ,only first of multiple questions to be answered . Please post remaining questions separately or post the same asking specific question number , Hope you understand. Thank You:) }