Q:

# Your parents will retire in 28 years. they currently have $280,000 saved, and they think they will need$1,750,000 at retirement. what annual interest rate must they earn to reach their goal, assuming they don't save any additional funds

Accepted Solution

A:
Since the type of interest is not listed: simple interest, 18.75%; compound interest, 6.8%.

Explanation:
For simple interest, the formula is I=prt, where I is the amount of interest earned, p is the amount of principal invested, r is the interest rate as a decimal number, and t is the amount of time.

Our amount of interest earned is 1,750,000-280,000=1,470,000. Our principal is 280,000 and our time is 28 years:
1470000=280000(r)(28)
1470000=7840000r.

Divide both dies by 7840000:
1470000/7840000 = 7840000r/7840000
0.1875 = r.

For compound interest, the formula is
$$A=p(1+r)^t$$,
where A is the total amount in the account, p is the amount of principal, r is the interest rate as a decimal number, and t is the amount of time.

Our total amount is 1,750,000, our principal is 280,000, and our time is 28: 1750000=280000(1+r)²⁸.

Divide both sides by 280,000:
1750000/280000 = (280000(1+r)²⁸)/280000
6.25=(1+r)²⁸.

To take the 28th root, we raise both sides to the 1/28 power: (1+r)=6.25^(1/28)
1+r = 1.0676.

Subtract 1 from both sides:
1+r-1=1.0676-1
r=0.0676, which rounds to 0.068.