Find the time it would take to earn $1600 in interest on an investment of $26,000 at a rate of 5.8%?

Question

Not sure how to set up to find T, please explain 

Answer 1

Is it compounded monthly yearly or continuously?

 

The Compound Interest Equation

P = C (1 + r/n)^nt
where
P = future value
C = initial deposit
r = interest rate (expressed as a fraction: eg. 0.06)
n = # of times per year interest in compounded
t = number of years invested
Simplified Compound Interest Equation

When interest is only compounded once per yer (n=1), the equation simplifies to:
P = C (1 + r)^t
Continuous Compound Interest

When interest is compounded continually (i.e. n --> ), the compound interest equation takes the form:
P = C e^rt

C=$26000

P=$26000+$1600

r=.058

need to find t 

 

if continuous compounding 

27600=26000e^(.058t)

 

first divide by 26000

1.061=e^(.058t)

 

when trying to solve for an exponent you need to use ln or other logs since we have an e use ln

 

ln(1.061)=ln(e^(.058t))=.058t

 

1.03 years =t 

 

just a a little over a year

 

if compounded annually 

 

P = C (1 + r)^t

 

27600=26000(1+.058)^t

1.06=(1+.058)^t

 

still need to use logs 

ln(1.06)=t•ln(1.058)

1.06 years =t 

Answer 2

Simple interest formula

 

SI=PRT

 

P=principle amount(initial investment)

R= rate of interest(in decimal)

T= No. of year

 

SI=1600

P=26000

R=5.8%=0.058

T=?

 

Substitute the values in formula

 

1600=26000*0.058* T

 

1600=1508 T

 

T=1.06100795 year