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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?

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  • $\begingroup$ What happens if you assume a principal value and perform the calculation from that? What about a different assumption of principal value? What do you notice about the results? $\endgroup$
    – Nij
    Commented Nov 2, 2019 at 4:21
  • $\begingroup$ @Nij Doing that results in different answers for the future value and compound interest, though the difference between the compound interest is 25.25 if the principal amount is 10k vs 11k $\endgroup$ Commented Nov 2, 2019 at 4:57
  • $\begingroup$ What about 12K, 13K, 14K, ... What is the pattern? Then, what causes it? $\endgroup$
    – Nij
    Commented Nov 2, 2019 at 6:19
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    $\begingroup$ If unknown leave it like that in a formula. $\endgroup$
    – Narasimham
    Commented Nov 2, 2019 at 10:37

1 Answer 1

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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

$$I = X(1+0.005)^5 - X = X\bigl((1+0.005)^5 - 1\bigr)$$

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