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ratelena [41]
3 years ago
6

7500 dollars is placed in an account with an annual interest rate of 7.75%. To the nearest year, how long will it take for the a

ccount value to reach 38200 dollars?
Mathematics
2 answers:
bazaltina [42]3 years ago
8 0

Answer:

It will take approximately 53 years for the account value to reach 38200 dollars

Step-by-step explanation:

Given the following parameters:

Principal P = 7500

Interest Rate R = 7.75% = 0.0775

Let us find the simple interest for the first year

Simple Interest, I = PRT

with T = 1 year = 12 months

I = 7500 × 0.0775 × 1

= 581.25

The amount for the first year is the addition of the principal and simple interest.

Amount, A = 7500 + 581.25 = 8081.25.

Now, we want to find the time T when Amount A = 38200

Given A = P + I

And I = PRT

A = P + PRT

= P(1 + RT)

Let us make T the subject of the formula.

Dividing both sides by P

A/P = 1 + RT

A/P - 1 = RT

T = ((A/P) - 1)/R

T = ((38200/7500) - 1)/0.0775

= (307/75)/0.0775

= 52.8172043

≈ 53 years.

MakcuM [25]3 years ago
5 0

Answer:

It will take 55 years for the account value to reach 38200 dollars

Step-by-step explanation:

This is a simple interest problem.

The simple interest formula is given by:

E = P*I*t

In which E are the earnings, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.

After t years, the total amount of money is:

T = E + P.

In this problem, we ahve that:

T = 38200, P = 7500, I = 0.075

So

First we find how much we have to earn in interest.

38200 = E + 7500.

E = 38200 - 7500

E = 30700

How much time to earn this interest?

E = P*I*t

30700 = 7500*0.075*t

t = \frac{30700}{7500*0.075}

t = 54.6

Rounding up

It will take 55 years for the account value to reach 38200 dollars

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