Question

slyes grandparents invest $1500 in a college account earns 4.9% intrest that is compound annually. how much money will be in the account after 10 years?

Answer 1

To calculate the future value of a $1500 investment after 10 years with an annual compound interest rate of 4.9%, you use the compound interest formula A = P(1 + r/n)^(nt). After plugging in the values and performing the calculations, the resulting amount will be approximately $2443.34.

Step-by-step explanation:

The question deals with the calculation of the future value of an investment using the formula for compound interest. To find out how much money will be in the account after 10 years, we use the formula:

`A = P(1 + r/n)^((nt))`

Where:

• A is the amount of money accumulated after n years, including interest.
• P is the principal amount (the initial amount of money).
• r is the annual interest rate (decimal).
• n is the number of times that interest is compounded per year.
• t is the time the money is invested for, in years.

In this case, the principal amount P is $1500, the annual interest rate r is 4.9% or 0.049 (as a decimal), and it's compounded yearly so n is 1. The time t is 10 years.

Substituting these values into the formula we get:

`A = 1500(1 + 0.049/1)^((1*10))`

Calculating the values, we get:

`A = 1500(1 + 0.049)^(10)`

`A = 1500(1.049)^(10)`

A ≈ 1500(1.62889)

A ≈ $2443.34

Therefore, after 10 years, the amount of money in the account, thanks to the power of compound interest, will be approximately $2443.34.

Answer 2

`\$2,420.17`

Step-by-step explanation:

we know that

The compound interest formula is equal to

`A=P(1+(r)/(n))^(nt)`

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

`t=10\ years\\ P=\$1,500\\ r=4.9\%=4.9/100=0.049\\n=1`

substitute in the formula above

`A=1,500(1+(0.049)/(1))^(1*10)`

`A=1,500(1.049)^(10)`

`A=\$2,420.17`