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Cameron invested $690 in an account paying an interest rate of 9, start fraction, 5, divided by, 8, end fraction9 8 5 ​ % compounded monthly. alonso invested $690 in an account paying an interest rate of 10, one eigth10 8 1 ​ % compounded continuously. to the nearest dollar, how much money would alonso have in his account when cameron's money has tripled in value?

User LOAS
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Final answer:

To find out how much money Alonso would have in his account when Cameron's money has tripled in value, we need to use the formula for compound interest. Cameron's money after tripling is $2070. Using the formula for continuous compounding, Alonso would have approximately $2070 in his account when Cameron's money has tripled after 7.53 years.

Step-by-step explanation:

To find out how much money Alonso would have in his account when Cameron's money has tripled in value, we need to use the formula for compound interest.

Let's first calculate how much money Cameron would have when his money triples. If Cameron's initial investment is $690, then his final amount, after tripling, would be $690 * 3 = $2070.

Now, let's calculate how much money Alonso would have using continuous compounding. The formula for compound interest with continuous compounding is given by the formula A = P * e^(rt), where A is the final amount, P is the initial principal, e is the base of the natural logarithm, r is the interest rate, and t is the time in years.

We know that P = $690, r = 10 8 1%, and t is the time needed for Alonso's money to triple. Since we are given the interest rate in a different form, we need to convert it into decimal form. 10 8 1% = 0.1081. We also know that A = $2070. We can rearrange the formula to solve for t: t = ln(A/P)/(r).

Plugging in the values, we get: t = ln($2070/$690)/(0.1081) = 7.53 years.

Therefore, Alonso would have approximately $2070 in his account when Cameron's money has tripled.

User Ddsultan
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