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4. Joe deposits $2,000 into a savings account. The account compounds his money quarterly at a rate of 4%. a) How much money does Joe have after a year? Round your answer to the nearest ten cents. b) After 18 months? Round your answer to the nearest dollar. c) When will his account grow to $25,000? Round your answer to the nearest year.

User Fairlie
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8 votes

Answer:

Explanation:

Formula to be used,

Final amount =
\text{Initial amount}*(1+(r)/(n))^(nt)

r = rate of interest

n = number of compounding in a year

t = Duration of investment in years

Initial amount = $2000

r = 4% = 0.04

n = 4

A). Final amount =
2000(1+(0.04)/(4))^(4* 1)

= 2000(1.01)⁴

= 2081.21

$2081

B). If t = 18 months ≈ 1.5 years

Final amount =
2000(1.01)^(4* 1.5)

=
2000(1.01)^6

= 2123.04

$2123

C). If final amount = $25000

25000 =
2000(1.01)^(4* t)


(25)/(2)=(1.01)^(4t)

12.5 =
(1.040604)^t

log(12.5) =
\text{log}(1.040604)^t

log(12.5) = t[log(1.040604)]

t =
\frac{\text{log}(12.5)}{\text{log}(1.040604)}

= 63.458

64 years

User JockX
by
8.3k points

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