Question

What annual rate of interest would you have to earn on an investment of $4500 to ensure receiving $292.50 interest after 1 year?

Answer 1

You want $4,792.50 after 1 year.

Total = 4,792.50 * (1 + rate)^1

Solving for the rate the formula is:
log(1 + rate) = {log(total) -log(Principal)} ÷ Years
(page for that formula: http://www.1728.org/compint2.htm

log(1 + rate) = log (4792.50) - log (4500) / years

log(4,792.50) = 3.6805621216
log (4500) = 3.6532125138
(years = 1 and doesn't need to be entered).

log(1 + rate) = 3.6805621216  -3.6532125138

log(1 + rate) = 0.0273496078

10^ 0.0273496078 = 1.065

Interest rate = 6.5%

Double Check
Total = 4,500 * (1.065)^1 = 4,792.50