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,

Question

forsale

10 days ago

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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:

zzz [11.8K] · Answer 1 · 2026-03-30T15:36:58+03:00

It’s understood that

The formula for calculating simple interest can be expressed as

$F=P*(1+n*r)$

where

F refers to the future value

P denotes the present value

n represents the number of years

r is the annual interest rate as a decimal

In the context of this problem

the values we are given are

$P=$ $ $3,900$

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

$F=$ $ $10,000$

To solve for 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 final result is the option

$c. 20 years$

AnnZ [11.9K] · Answer 2 · 2026-03-30T15:39:28+03:00

To determine the future value using simple interest, the formula is: future value = present value (1+n*rate), where n represents the number of years and rate indicates the annual interest as a decimal. By substituting the values into the equation, we find that 10000 = 3900(1 + 0.0783*t). Therefore, we calculate 1 + 0.0783t = 10000/3900, leading to t = (10000/3900 - 1)/0.0783, which equals approximately 19.98 years. For compound interest, the future value is determined by present value (1 + rate/n)^(nt), where n=1, rate=0.0783, future value=10000, present value=3900, ultimately resulting in t = log(10000/3900)/log(1.0783) which yields roughly 12.49 years.