Question

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.​

Answer 1

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}`