John invested his money in a time deposit that pays $0.5\%$ compound interest in a year. How much will his money be after $5$ years? How much interest will he gain?
Given:
Rate ($r$): $0.5\%$ or $0.005$
Time ($t$): $5$ years
Principal Amount ($P$): ?
Maturity (Future) Value ($F$): ?
Compound Interest ($I$): ?
In compound interest we were taught two formulas
$$F = P(1+r)^t$$ $$I = F - P$$
I'm stuck on this because there are two missing values in the Future value formula, the book did not give a principal amount, or any indication of how much money he invested. I assume we are supposed to derive something but I'm stuck. Can anyone help?
Well, based on the information given, there is no way to tell how much money he will have in $5$ years. The best attempt at answering your question would be to assume some arbitrary amount, say $X$, and then do the calculations:
$$F = X(1+0.005)^5$$ And
$$I = X(1+0.005)^5 - X = X\bigl((1+0.005)^5 - 1\bigr)$$