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Your grandparents invested $2,000 for you on the day you were born. How much will this investment be worth on your 25th birthday if the money was invested in a savings account averaging an annual yield of 5% and the interest is compounded quarterly?

Please answer this correctly.​

User TheSchwa
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1 Answer

6 votes

We know that, Amount in Compound interest is given by :


\bigstar \ \ \boxed{\sf{Amount = Principal\bigg(1 + (Rate \ of \ Interest)/(100)\bigg)^(Time \ Period)}}

Given : Principal = $2000

Given : Annual yield is 5% and the interest is compounded quarterly

It means : Interest is compounded 4 times in a year


\implies \sf{Rate \ of \ Interest = (R)/(4) = (5)/(4)}


\sf{\implies Time \ period = (25 * 4) = 100}

Substituting all the values in the formula, we get :


\implies \sf{Amount = 2000\bigg(1 + ((5)/(4))/(100)\bigg)^(100)}


\implies \sf{Amount = 2000\bigg(1 + (5)/(400)\bigg)^(100)}


\implies \sf{Amount = 2000\bigg(1 + (1)/(80)\bigg)^(100)}


\implies \sf{Amount = 2000\bigg((81)/(80)\bigg)^(100)}


\implies \sf{Amount = 2000 * (1.0125)^(100)}


\implies \sf{Amount = 2000 * 3.463}}


\implies \sf{Amount = 6926.8}

User Neil John Ramal
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