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Dima020 [189]
3 years ago
9

If you invest $3,900 at a 7.83% simple annual interest rate, approximately how long will it take for you to have a total of $10,

000? a. 12 years b. 15 years c. 20 years d. 30 years
Mathematics
2 answers:
ch4aika [34]3 years ago
7 0

we know that

The simple interest formula is equal to

F=P*(1+n*r)

where

F is the future value

P is the present value

n is the number of years

r is the annual interest rate in decimal

In this problem

we have

P=$3,900

r=7.83% -----> r=0.0783

F=$10,000

Find the value of n

F=P*(1+n*r)\\ \\ \frac{F}{P} =1+n*r\\ \\ n=\frac{(\frac{F}{P}-1)}{r}  \\ \\ n=\frac{(\frac{10,000}{3,900}-1)}{0.0783}\\ \\ n=19.98 years

therefore

the answer is the option

c. 20 years

densk [106]3 years ago
4 0
Apply simple interest formula
future value = present value (1+n*rate)
n=number of years
rate = annual interest rate in decimal

Plug in values,
10000=3900(1+0.0783*t)
1+0.0783t=10000/3900
t=(10000/3900-1)/0.0783
=19.98 years.

With compound interest,  future value=present value (1+rate/n)^(nt)
n=1,rate=0.0783, future value=10000, present value=3900,
t=log(10000/3900)/log(1.0783)=12.49 years.
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