Science Math Word Problem

Question

Miguel starts a job working as a biochemist and earns $76,500 a year. He saves 10 percent of his income. After working for one year, he invests what he has saved in an account that pays 2.5 percent interest, compounded quarterly. How much money will be in this account 10 years after his initial investment?

Answer 1

Hi Vince, the formula for the amount after a period of time is:

 

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

 

Where:

 

A is the amount in the account

P is the original investment

r is the interest rate

n is the number of times compounded

t is the time in years

 

Step 1:

 

Find the original investment. Miguel saves 10 percent of his income. 10% of $76,500 is $7650.

 

Step 2:

 

Find A.

 

A = 7650 * ( 1 + .025 / 4)^{(4 * 10)}

 

A = 7650 * (1 + .00625)⁴⁰

 

A = 7650 * 1.00625⁴⁰

 

A ≈ 7650 * 1.283

 

A ≈ 9814.95

 

After 10 years, the account would be worth approximately $9814.95.

 

Questions?