Question

100 points. You earned $1600 in interest in your savings account over 10 years at a rate of 8%. How much money did you originally deposit into your savings account?

Answer 1

A = p(1+r)^t

1600 = p(1+0.08)¹⁰

P = 1600/2.1589

P= 741.12

741.12 dollar money did you originally deposit into your savings account!

Answer 2

Answer:

Simple interest:  Principal = $2000

Annual compound interest:  Principal = $1380.59

Step-by-step explanation:

As the question does not stipulate which type of interest was applied, please find below calculations for both simple interest and annual compound interest.

Simple Interest Formula

I = Prt

where:

• I = interest accrued
• P = principal
• r = interest rate (in decimal form)
• t = time (in years)

Given:

• I = $1600
• r = 8% = 0.08
• t = 10 years

Substitute the given values into the formula and solve for P:

$\implies \sf 1600=P(0.08)(10)$

$\implies \sf 1600=0.8P$

$\implies \sf P=\dfrac{1600}{0.8}$

$\implies \sf P=2000$

Therefore, the initial deposit (principal) was $2000.

.....................................................................................................

Annual Compound Interest Formula

$\large \text{ \sf I=P\left[\left(1+r\right)^{t} -1\right] }$

where:

• I = interest accrued
• P = principal amount
• r = interest rate (in decimal form)
• t = time (in years)

Given:

• I = $1600
• r = 8% = 0.08
• t = 10 years

Substitute the given values into the formula and solve for P:

$\implies \sf 1600=P\left[\left(1+0.08)^{10}-1\right]$

$\implies \sf 1600=P\left[\left(1.08)^{10}-1\right]$

$\implies \sf 1600=P\left[2.15892...-1\right]$

$\implies \sf 1600=P\left[1.15892...\right]$

$\implies \sf P=\dfrac{1600}{1.15892...}$

$\implies \sf P=1380.5897...$

Therefore, the initial deposit (principal) was $1380.59 (nearest cent).

Learn more about simple interest here:

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Learn more about compound interest here:

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