3. $10,000 is invested in a college fund on a child\'s birthday. If the total co

Question

3. $10,000 is invested in a college fund on a child's birthday. If the total cost of college is $45,000, what interest rate, compounded annually, must the fund earn in order to be able to pay for college tuition on her 18th birthday (after 18 years)? 4, $20,000 is invested in an index fund earning 8% interest. After how long will the fund be worth $36,000, if interest is compounded monthly? What is the effective interest rate? a. fter how long will the fund be worth $36,000, if interest is compounded continuously? What is the effective interest rate? b. A

Explanation / Answer

3. Here, principal, P = $ 10000, amount to be paid after 18 years, A = $ 45000 and time, t = 18 years.

Let the required rate = r% per annum

Now we have, A = P [1+r/100]^t

=> 45000 = 10000 [1+r/100]^18

=> 4.5 = (1+r/100)^18

=> (4.5)^1/18 = 1+r/100

=> 1+r/100 = 1.087 => r/100 = 1.087 - 1 = 0.087

=> r = 100×0.087 = 8.7

Thus required rate, r = 8.7%

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