Question

Six months ago, a friend of yours lost the login information to an online account that she owns, which has holdings of a digital currency (the account information was stored on a hard drive, which she lost). The last time she viewed the account, its value in US dollars was $65,000. Since that time, the value of a unit of the digital currency has increased steadily, by 6% each month. If this 6% rate of return continues for another six months, and your friend is able to regain access to her account by then, what will be the dollar value of her account at that time (rounded to the nearest dollar)?

A. $92,204
B. $130,793
C. $319,626
D. $453,396
E. $544,950

Answer 1

Using the compound interest formula, the future value of the account is calculated to be $92,204 after another six months of a 6% monthly increase in the value of the digital currency, which corresponds to option A.

Step-by-step explanation:

To calculate the new value of your friend's digital currency holdings after six months of a steady 6% monthly increase, we need to use the compound interest formula:A = P(1 + r)^nwhere:A is the amount of money accumulated after n months, including interest.P is the principal amount (the initial amount of money before interest).r is the monthly interest rate (in decimal form).n is the number of times that interest is compounded per month.

Given that:P = $65,000 (the initial value of the account)r = 6% per month, which is 0.06 when expressed as a decimaln = 6 (the total number of months for the interest to be applied)

Substituting these values into the formula gives us:
A = $65,000(1 + 0.06)^6

Calculating the above expression, we get:
A = $65,000 * (1.06)^6
A = $65,000 * 1.418519
A = $92,203.74 which, rounded to the nearest dollar, is $92,204. Therefore, if the value of the digital currency continues to increase at a rate of 6% per month, the dollar value of her account after another six months will be $92,204, which corresponds to option A.