17. The future value (A) for some principal (P), interest rate (r), number of compoundings per year (n), and number of years (t) is given by
... A = P(1 + r/n)^(nt)
You have P=45000, r=.08, n=4, t=3, so the balance in the account is
... A = $45000(1.02^12) = $57,070.88 . . . . part (a)
The amount of this that is interest is the excess over the initial investment.
... I = A - P = $57,070.88 - 45,000.00 = $12,070.88 . . . . part (b)
21. The equation for simple interest is
... I = P·r·t = $25,000·0.10·1 = $2,500 . . . . . amount sister will pay
Using the equations above, we find the interest the bank will pay is
... I = $25,000(1 +.06/4)^(4·1) - 25,000 = $25,000·1.0613636 - 25,000 = $1,534.09
The simple interest investment will generate more interest in the amount of
... $2500 - 1534.09 = $965.91 . . . . additional interest from 10% investment
The effective annual rate for the simple interest loan is 10.00%.
The effective annual rate for the compound interest loan is 1534.09/25000 ≈ 6.14%.