Question

You love the number “7” and you consider it very lucky. Your goal is to deposit a lump sum into a savings account that pays 7% compounded annual interest and leave the money in the account for exactly 7 years, at which time you will withdraw the entire amount, since its value at that moment will be exactly $7,777.77The bank is even willing to accommodate you by compounding the interest 7 times a year, instead of its usual monthly compounding (12 times per year). How much money do you deposit today, so that you have $7,777.77 seven years later?

Answer 1

Let's use the compound interest formula:

$A=P(1+\frac{r}{n})^{nt}$

Where:

A = Amount = 7777.77

P = Principal

r = Interest rate = 7% = 0.07

t = time = 7

n = Number of times interest is compounded per unit t = 7

Therefore:

$\begin{gathered} 7777.77=P(1+\frac{0.07}{7})^{7\cdot7} \\ 7777.77=P(1.628) \\ solve_{\text{ }}for_{\text{ }}P\colon \\ P=\frac{7777.77}{1.628} \\ P=4776.477991 \\ P\approx4776.48 \end{gathered}$

Answer:

$4776.48