Sergio Math Problem

Question

Sergio has decided to diversify his investments in the following way: $4,000 in an account earning 3.2% simple interest $4,000 in a savings account earning 2.1% interest compounded annually $7,500 in a certificate of deposit earning 5% interest compounded quarterly How much total interest will Sergio earn on his investments at the end of 4 years? 

Answer 1

 

The compound interest formula is: 

 

     A = P(1 + r/n)^nt

 

     A = Amount of money accumulated

     P = Principal amount invested

     r = annual interest rate

     n = number of compounds per year

     t = time, in years

 

For our scenario,

 

     P = 4000

     r = 2.1% = .021

     n = 4 ... compounded quarterly, 4 times per year

     t = 4 ... number of years

 

     A = 4000(1 + .021/4)⁴⁽⁴⁾

 

     A = 4000(1.021)¹⁶

 

     A = 4000(1.39447866269)

 

     A = $ 5,577.91

 

After 4 years he will have accumulated $5577.91

 

However, the question asked for amount of interest earned, so we have to subtract 4,000.

 

Total interest earned is $1,577.91