Calculate the future value of an investment using simple and compound interest formulas.

This question involves simple interest. The formula for simple interest is $I = PRT$, where:

• $I$ is the total interest earned.
• $P$ is the principal amount (initial investment).
• $R$ is the annual interest rate (as a decimal).
• $T$ is the time in years.

Given:

• P = \500$
• $R = 1.7\% = 0.017$
• $T = 10$ years

Substitute these values into the formula: $I = \$500 \times 0.017 \times 10$ $I = \$85$

This question involves compound interest, compounded daily. The formula for compound interest is $A = P(1 + \frac{r}{n})^{nt}$, where:

• $A$ is the final amount.
• $P$ is the principal amount (initial investment).
• $r$ is the annual interest rate (as a decimal).
• $n$ is the number of times interest is compounded per year.
• $t$ is the time in years.

Given:

• P = \200$
• Daily interest rate $= 0.0035\%$
• Time $= 1$ year $= 365$ days

First, convert the daily interest rate to a decimal:
Daily rate $= 0.0035\% = \frac{0.0035}{100} = 0.000035$

Since the interest is compounded daily, the number of compounding periods is $n = 365$ (days in 1 year).
The interest rate given is already a per-day rate, so we can use it directly in the compound interest formula where $r/n$ becomes the daily rate and $nt$ becomes the total number of days.
Let $i_{day}$ be the daily interest rate.
The formula simplifies to $A = P(1 + i_{day})^{\text{number of days}}$.

Substitute the values: $A = \$200 (1 + 0.000035)^{365}$ $A = \$200 (1.000035)^{365}$ Calculate the value inside the parenthesis:

$$(1.000035)^{365} \approx 1.01285$$

Now, multiply by the principal: $A = \$200 \times 1.01285$ $A \approx \$202.57$

c)

i) The total interest earned is \boxed{\85}$.

ii) The value of Ollie's investment at the end of 1 year is \boxed{\202.57}$.

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