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Ruby invested $850 in an account paying an interest rate of 2 7/8%compoundedquarterly. Logan invested $850 in an account paying an interest rate of 2 3/8%compounded monthly. After 17 years, how much more money would Ruby have inher account than Logan, to the nearest dollar?

User Emese
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1 Answer

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We would apply the formula for determining compound interest. It is expressed as

A = P(1 + r/n)^nt

Where

A = total amount in the account after t years

r represents the interest rate

n represents the periodic interval at which it was compounded

P represents the principa or amount invested.

Considering Ruby's investment,

P = 850

r = 2 7/8 = 2.875/100 = 0.02875

n = 4 because it was compounded 4 times in a year

t = 17 years

Therefore,

A = 850(1 + 0.02875/4)^4 * 17

A = 850(1 + 0.0071875)^68

A = 1383.315

For Logan's investment,

P = 850

r = 2 3/8 = 2.375/100 = 0.02375

n = 12 because it was compounded 12 times in a year

t = 17 years

Therefore,

A = 850(1 + 0.02375/12)^12 * 17

A = 850(1 + 0.00197916667)^204

A = 1272.307

The difference between Ruby's return and Logan's return is

1383.315 - 1272.307 = 111.008

Rounding to the nearest dollar, it becomes $111

Therefore, Ruby has $111 in her account more than Logan