Timmy wants to invest a sum of money in one of the following investment plans.

Plan	Description
Plan A	Pays 2% simple interest per year
Plan B	Pays 2% compound interest per year

Which investment plan is the better choice for Timmy? Explain your answer. Answer : ... ... Mary deposits $8000 in a savings account at a simple interest rate of 3.5% per year. Calculate the total value of her savings at the end of 12 years. Answer $ ... Peter invested $50 000 in an investment plan from 2010 to 2024.
The value of his investment increased by $r\%$ at the end of every year.
At the end of 2024, the total value of Peter's investment is $65 320. Calculate the value of $r$. Answer $r$ = ... (d) The current exchange rate between Singapore dollars (SGD) and Thailand baht (THB) is given as SGD 1 = THB 27.16. Susan bought a bag while shopping in Thailand. The original price of the bag was THB 56 000 and Susan bought it at a 15% discount. Susan paid for the bag using her credit card which charged her an additional 2% fee for overseas transaction. Calculate the total amount, including credit card fee, that Susan had to pay in Singapore dollars (SGD). Correct your answer to the nearest cent. Answer $ ...

1. Choose the better investment plan and justify using the meaning of compound interest

Both plans have the same annual rate of $2\%$. Plan B is better because compound interest is calculated on the accumulated amount each year, while simple interest is calculated only on the original sum.

1. Calculate the simple interest earned over 12 years

Simple interest
$= 8000 \times \frac{3.5}{100} \times 12$
$= 3360$

2. Add the interest to the original deposit to find the total value

Total value
$= 8000 + 3360$
$= 11360$

1. Set up the compound growth equation for 14 yearly increases

From 2010 to 2024, there are $2024-2010=14$ yearly increases.

Let the yearly multiplier be $1+\dfrac{r}{100}$.

$50000\left(1+\frac{r}{100}\right)^{14}=65320$

2. Isolate the yearly growth multiplier

$\left(1+\frac{r}{100}\right)^{14}=\frac{65320}{50000}$

$1+\frac{r}{100}=\left(\frac{65320}{50000}\right)^{\frac{1}{14}}$

3. Calculate the percentage rate $r$

$\frac{r}{100}=\left(\frac{65320}{50000}\right)^{\frac{1}{14}}-1$

$r=100\left[\left(\frac{65320}{50000}\right)^{\frac{1}{14}}-1\right]$

$r\approx 1.920$

1. Find the discounted price of the bag in THB

A 15% discount means Susan pays $100\%-15\%=85\%$ of the original price.

$56000\times 0.85=47600$

Discounted price $=\text{THB }47600$

2. Include the 2% overseas transaction fee

A 2% fee means Susan pays $100\%+2\%=102\%$ of the discounted price.

$47600\times 1.02=48552$

Total charged $=\text{THB }48552$

3. Convert the total amount from THB to SGD and round to the nearest cent

Since SGD 1 = THB 27.16,

$\text{Amount in SGD}=48552\div 27.16=1788.953\ldots$

Correct to the nearest cent, this is $\char36{}1788.95$.