Question

Phyllis invested $13,000, a portion earning a simple interest rate of 5¼% per year and the rest earning a rate of 5% per year. After one year the total interest earned on these investments was $672.50. How much money did she invest at each rate?

Answer 1

Answer:

Phyllis invested $9000 at the rate of 5.25% and $4000 at the rate of 5%.

Step-by-step explanation:

Formula for the simple interest is,

Interest = $\frac{P\times r\times t}{100}$

Here, P = Principal amount

r = rate of interest  

t = Duration of investment

Let Phyllis invested amount (at 5.25% rate of interest) = $x

Therefore, Interest on this amount,

Interest = $\frac{5.25\times x}{100}$

             = $0.0525x

If he invested the rest amount $(13000 - x) at the rate of 5%,

Interest earned on this amount = $\frac{(13000-x)\times 5\times 1}{100}$

                                                    = $(650 - 0.05x)

Interest earned on total amount = $672

Therefore, $0.0525x + $(650 - 0.05x) = $672.5

0.0025x + 650 = 672.5

0.0025x = 22.5

x = $9000

Rest amount = 13000 - 9000

                     = $4000

Phyllis invested $9000 at the rate of 5.25% and $4000 at the rate of 5%.