What is the ending amount for a deposit of $2,000 in an account with a 1.34% interest rate, compounding semiannually, in 10 year
s?
1 answer:
Answer:
$2,285.76
Step-by-step explanation:
Year Year Interest Total Interest Balance
1 $26.89 $26.89 $2,026.89
2 $27.25 $54.14 $2,054.14
3 $27.62 $81.76 $2,081.76
4 $27.99 $109.75 $2,109.75
5 $28.37 $138.11 $2,138.11
6 $28.75 $166.86 $2,166.86
7 $29.13 $195.99 $2,195.99
8 $29.52 $225.52 $2,225.52
9 $29.92 $255.44 $2,255.44
10 $30.32 $285.76 $2,285.76
Base amount: $2,000.00
Interest Rate: 1.34% (yearly)
Effective Annual Rate: 1.34%
Calculation period: 10 years
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In geometry, it would be always helpful to draw a diagram to illustrate the given problem.
This will also help to identify solutions, or discover missing information.
A figure is drawn for right triangle ABC, right-angled at B.
The altitude is drawn from the right-angled vertex B to the hypotenuse AC, dividing AC into two segments of length x and 4x.
We will be using the first two of the three metric relations of right triangles.
(1) BC^2=CD*CA (similarly, AB^2=AD*AC)
(2) BD^2=CD*DA
(3) CB*BA = BD*AC
Part (A)
From relation (2), we know that
BD^2=CD*DA
substitute values
8^2=x*(4x) => 4x^2=64, x^2=16, x=4
so CD=4, DA=4*4=16 (and AC=16+4=20)
Part (B)
Using relation (1)
AB^2=AD*AC
again, substitute values
AB^2=16*20=320=8^2*5
=>
AB
=sqrt(8^2*5)
=8sqrt(5)
=17.89 (approximately)
