Nolan invested $5,300 in an account paying an interest rate of 3.8% compounded annually. Assuming no deposits or withdrawals are

Question

2 years ago

12

made, how long would it take, to the nearest tenth of a year, for the value of the account to reach $6,880?

1 answer:

Sveta_85 [38] · Answer 1 · 2023-02-03T19:25:45+03:00

It will take Nolan 7 years compounded annually at the rate of 3% for his money to reach $6880

To solve this problem, we would use the formula of compound interest.

Data given;

<h3>Compound Interest</h3>

The formula used in calculating compound interest is given as

$A = P(1 + r/n)^n^t$

let us plug in the values and solve for t.

$6880 = 5300(1 + \frac{0.038}{1})^1^*^t\\
 \frac{6880}{5300}=(1+0.038)^t\\
 1.29=(1.038)^t$

Take the natural log of both sides

$ln(1.29)=ln(1.038)^t\\
0.25=t*0.037\\
t=0.25/0.037\\
t=6.75\\
t=7$

The time it will take for $5330 compounded annually at the rate of 3% is 7 years.

Learn more on compound interest here;