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

Answer:

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

Step-by-step 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.

$4.5\%=\frac{4.5}{100}=0.045$

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

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

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

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

Therefore, Vanore will have $1225 after 5 years.

Let us convert 4% interest rate in decimal for.

$4\%=\frac{4}{100}=0.04$

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

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

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

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

Therefore, Keir will have $1440 after 5 years.

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

$A=P(1+\frac{r}{n})^{n*T}$, 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.

$6\%=\frac{6}{100}=0.06$

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

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

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

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

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

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.