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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
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Jan 6, 2019
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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
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Rising Lee
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Since the type of interest is not listed: simple interest, 18.75%; compound interest, 6.8%.
Step-by-step 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
,
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.
HankSmackHood
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Jan 12, 2019
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HankSmackHood
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