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Question 3 (20 marks)
1. You need $3,000 to buy a new stereo for your car in 3 years. What value you must have now if the compounded annually return is 10%.
2. Your grandfather placed $5,000 in a trust fund for you. In 12 years what will be the worth of the savings. If the estimated rate of return on the trust fund is 8%?

Respuesta :

1. At 10% compounded interest for three years, the value of investing $3,000 to buy new audio for your automobile is $2,253.94.

2. Compound interest on a $5,000.00 principal at an annual rate of 8% compounded once a year for 12 years equals $12,590.85.

What are the calculation steps?

Calculation of Compound interest

Given Data

Principal = $5,000

Time = 12 years

Rate = 8%

Assuming a compounded interest approach

A = P + I

where;

P (principal) = $5,000.00

I (interest) = $7,590.85

Calculation Steps:

First, convert R as a percent to "r" as a "decimal"

[tex]r = \frac{R}{100}\\\\r = \frac{8}{100}\\\\r = 0.08 \text{ rate per year}[/tex]

Then solve the "equation for A"

[tex]A = P(1 + \frac{r}{n}) nt\\\\A = 5,000.00(1 + \frac{0.08}{1})(1)(12)\\\\A = 5,000.00(1 + 0.08)(12)\\\\A = 12,590.85[/tex]

Thus, at 10% compounded interest for three years, the value of investing $3,000 to buy a new radio for your car is $2,253.94, whereas the fund in which the grandfather invested $5,000 at an 8% rate of return will be worth $12,590.85 in 12 years.

Check out the link below to learn more about the annual rate of return;

https://brainly.com/question/15057277

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