Question

1. First City Bank pays 7 percent simple interest on its savings account balances, whereas Second City Bank pays 7 percent interest compounded annually. If you made a deposit of $16,000 in each bank, how much more money would you earn from your Second City Bank account at the end of 11 years? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Difference ____________

2. Assume that in 2014, an 1872 $20 double eagle sold for $15,600.

What was the rate of return on this investment? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Rate of return ____________

3.

An investment offers to double your money in 24 months (don’t believe it).

What rate per year are you being offered? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Rate _________________   

Answer 1

Ans: r = rate of interest = 7% , Number of years = n = 11 years

Simple Interest = 16,000 * 7% * 11 years = 12,320

Compound Interest = PV * (1+r)ⁿ

= 16,000 * (1+7%)¹¹

= 16,000 * (1+0.07)¹¹

= 16,000 * 2.1048

= 33,677.63

Difference in interest earned 32,677.63 - 12,320 = $ 21,357.63

2. FV = PV (1+r)^t , 2014 - 1872 = 142

15,600 = 20 * (1+r)¹⁴²

15,600/20 = (1+r)¹⁴²

780 = (1+r)¹⁴²

(1+r) = 780^1/142

1+r = 1.048013

r = 4.80 %

3. FV = PV * (1+r)^t

PV = 1, FV = 2 , t = 2 years

2 = (1+r)²

2 ^1/2 = (1+r)

1.4142 = (1+r)

r = 41.42 %