Wayne inherited a sum of money from his parents. He decided to invest 60% of the money and shares $\frac{3}{4}$ of the remaining amount with his wife.
The other $20 000 are meant for their travelling expenses.
Calculate the sum of money he inherited. Answer $ ___ A bank offers two investment packages. Wayne wants to invest $55 000 in one of the packages for 3 years.
Which package should he choose if he wishes to reap the most benefits from the investment? Wayne and his wife go on a seven days self-drive trip to Australia. They pay 150 AUD per day for car hire and 380 AUD per night for hotel.
They pay using credit card and is charged with a fee of 2% for the currency conversion.
The exchange rate between Singapore dollars and Australian dollars is $1 = 0.91 AUD.
Calculate the total amount, including credit card fee, Wayne is charged for car hire and accommodation.
Give your answer in Singapore dollars, correct to the nearest dollar. Answer $ ___

1. Represent the inherited sum and find the amount remaining after investing 60%.

Let the sum of money inherited be $x$.\n\nWayne invests $60\%$ of the money, so the remaining amount is\n$100\% - 60\% = 40\%$\n$= 0.4x$

2. Identify the fraction of the remaining amount used for travelling expenses.

He shares $\dfrac{3}{4}$ of the remaining amount with his wife.\n\nSo the fraction of the remaining amount left for travelling expenses is\n$1 - \frac{3}{4} = \frac{1}{4}$\n\nTravelling expenses amount:\n$\frac{1}{4}(0.4x) = 20000$

3. Solve the equation to find the inherited sum.

$\frac{1}{4}(0.4x)=20000$\n$0.1x=20000$\n$x=\frac{20000}{0.1}=200000$\n\nTherefore, Wayne inherited $200 000.

1. Calculate the simple interest earned from Package A over 3 years.

For Package A,
$\text{Simple interest}=55000\times \frac{0.97}{100}\times 3$
$=\$1600.50$

2. Calculate the one-time payout and hence the total benefit from Package A.

One-time payout:
$10\%\text{ of }55000=55000\times \frac{10}{100}=\$5500$
Total benefit from Package A:
$1600.50+5500=\$7100.50$

3. Calculate the final amount for Package B using compound interest over 3 years.

For Package B,
$\text{Final amount}=55000\left(1+\frac{3.78}{100}\right)^3$
$=55000(1.0378)^3$
$=\$61475.73\text{ approximately}$

4. Find Package B's benefit and compare both packages.

Benefit from Package B:
$61475.73-55000=\$6475.73$
Compare:
$\$7100.50>\$6475.73$
Therefore, Package A gives the greater benefit.