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aivan3 [116]
3 years ago
12

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.​
Mathematics
1 answer:
algol [13]3 years ago
8 0

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

\bigstar \ \ \boxed{\sf{Amount = Principal\bigg(1 + \dfrac{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 = \dfrac{R}{4} = \dfrac{5}{4}}

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

Substituting all the values in the formula, we get :

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

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

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

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

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

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

\implies \sf{Amount = 6926.8}

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