Question

Nolan invested $5,300 in an account paying an interest rate of 3.8% compounded annually. Assuming no deposits or withdrawals are made, how long would it take, to the nearest tenth of a year, for the value of the account to reach $6,880?

Answer 1

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;

• A = 6880
• P = 5300
• r = 3.8 % = 0.038
• N = 1

Compound Interest

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.

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