Mathematics: Igraduated from high school and received $1500 in gifts from family and friends. you also received scholarships in the amount of $800. if you deposit the total amount received into a 24-month cd at 5.5% compounded daily, how much will you receive at the end of 24 months? b. how much interest did you earn on the investment?

Igraduated from high school and received $1500

kward591

07.01.2022

ANSWER:

At the end of 24 months we will receive $2566.135 as the interest earned on $2300 is $266.135.

SOLUTION:

Given, I graduated from high school and received $1500 in gifts from family and friends. You also received scholarships in the amount of $800.

Total amount received into a 24-month CD at 5.5% compounded daily.

We have to find how much will you receive at the end of 24 months.

Now, amount that is compounded daily is given by:

$\mathrm{A}=\mathrm{a}\left(1+\frac{r}{n}\right)_{}^{\mathrm{nt}}$ → (1)

where A is final amount and a is deposited amount

r is interest rate.

n is number of days

t is number of years

now, a = 1500 + 800 = 2300, r = 5.5%, n = 365 days per year, t = $\frac{24}{12}$ = 2 years.

Substitute above values in (1)

$\mathrm{A}=2300 \times\left(1+\frac{\frac{5.5}{100}}{365}\right)^{365 \times 2}$

$\begin{array}{l}{A=2300(1+0.000150)^{730}=2300(1.00015)^{70}} \\ {=2300 \times 1.11571=2566.1350}\end{array}$

So, in the end we will receive an amount of $2566.135.

Now, interest earned = received amount – deposited amount = 2566.135 – 2300 = $266.135

Hence, at the end of 24 months we will receive $2566.135 as the interest earned on $2300 is $266.135.

0,0(0 оценок)