We are now going to investigate the effects of doubling different variables in the compound interest formula.
a. Start by choosing a goal you want to save money for, such as a vacation or a big purchase. Decide how much money you would want to deposit as an initial investment (your principal).
Suppose you invest this money at 4% interest, compounded monthly, for 5 years. How much will you have in total?
b. Now let’s double the interest rate: you invest the same amount, but at 8% interest, compounded monthly, for 5 years. How much will you have saved?
c. Now let’s double the time, instead: invest the same amount, at 4% interest, for 10 years. How much have you saved?
d. Now let’s double the compounding period: invest the same amount, at 4% interest, for 5 years, but compounded semi-monthly (24 times a year). How much have you saved?
e. Finally, let’s double the principal: invest twice your original amount, at 4% interest, for 5 years, compounded monthly. How much have you saved?
f. Based on your calculations, which variable most influences compound interest when you double it?
g. If none of the above scenarios result in enough money to reach your goal, try to find out what interest rate you would need in order to reach your goal in the time period you want.