Question

Three friends decide that they each want to be able to buy a new boat in five years. Vanore puts $1,000 in a savings account with a simple interest rate of 4.5%. Keir invests $1,200 in a standard savers account with a simple interest rate of 4%. Omar invests $950 in a junior achievers account with a 6% annual compound interest rate. Who will have the most money to spend on a new boat at the end of the five years? Use the formula mc019-1.jpg for simple interest and mc019-2.jpg for compound interest. Round to the nearest dollar.

Answer 1

Keir will have the most money ($1440) to spend on a new boat at the end of the five years.

Explanation:

We have been given that three friends decide that they each want to be able to buy a new boat in five years.

Let us find the money earned by each friend after 5 years.

We will use simple interest formula to find the amount of money earned by Vanore and Keir.

`A=P(1+rt)`, where,

`A=\text{Final amount after T years}`,

`P=\text{Principal amount}`,

`r=\text{Interest rate in decimal form}`,

`T=\text{Time in years}`

Let us convert 4.5% interest rate in decimal for.

`4.5\%=(4.5)/(100)=0.045`

`\text{Amount of money earned by Vanore after 5 years}=1000(1+0.045*5)`

`\text{Amount of money Vanore will get after 5 years}=1000(1+0.225)`

`\text{Amount of money earned by Vanore after 5 years}=1000(1.225)`

`\text{Amount of money earned by Vanore after 5 years}=1225`

Therefore, Vanore will have $1225 after 5 years.

Let us convert 4% interest rate in decimal for.

`4\%=(4)/(100)=0.04`

`\text{Amount of money Keir will get after 5 years}=1200(1+0.04*5)`

`\text{Amount of money Keir will get after 5 years}=1200(1+0.2)`

`\text{Amount of money Keir will get after 5 years}=1200(1.2)`

`\text{Amount of money Keir will get after 5 years}=1440`

Therefore, Keir will have $1440 after 5 years.

We will use compound interest formula to find the amount of money earned by Omar.

`A=P(1+(r)/(n))^(n*T)`, where,

`A=\text{Final amount after T years}`,

`P=\text{Principal amount}`,

`r=\text{Interest rate in decimal form}`,

`n=\text{Number of times interest is compounded per year}`,

`T=\text{Time in years}`

Let us convert our given interest rate in decimal form.

`6\%=(6)/(100)=0.06`

`\text{Amount of money Omar will get after 5 years}=950(1+(0.06)/(1))^(1*5)`

`\text{Amount of money Omar will get after 5 years}=950(1+0.06)^(5)`

`\text{Amount of money Omar will get after 5 years}=950(1.06)^(5)`

`\text{Amount of money Omar will get after 5 years}=950*1.3382255776`

`\text{Amount of money Omar will get after 5 years}=1271.314`

Therefore, Omar will get $1271.314 after 5 years.

As $1440 is greater than $1225 and also than $1271.31, therefore, Keir will have the most money to spend on a new boat at the end of the five years.

Answer 2

To get the answer, you have to find the simple interest and compound interest.
Simple Interest= Principal amount(1+rate x time)
Compound interest= Principal amount(1 + rate/number of months)^number of months x time
simple interest Vanore= 1000(1+ 0.045x5)
=1225 dollars
simple interest Keir= 1200(1+ 0.04x5)
=1440 dollars
compound interest Omar= 950(1+ 0.06/12)^12(5)
=1281 dollars

The answer is Keir having 1440 dollars.