Question

If $2,500 is invested at 3% interest, how much money must be invested at 6% so that the total return for both investments is $180?

Answer 1

$ 1750 must be invested at 6% so that the total return for both investments is $180.

Step-by-step explanation:            

         1st Investment                                            2nd Investment

Given, Principal = $P_{1}$ = $ 2500                             Principal = $P_{2}$

Rate = $R_{1}$ = 3%                                              Rate = $R_{2}$ = 6%, Time = $T_{2}$ = 1 year

Time = $T_{1}$ = 1 year                                                   Interest = $I_{2}$

Simple Interest = $I_{1}$ = $\frac{PRT}{100}$ = $\frac{2500\times 3\times 1}{100}$ = $ 75

Total return from both investment = $ 180

=> $I_{1} + I_{2}$ = $ 180

=> $ 75 + $\frac{P_{2}R_{2}T_{2}}{100}$ = $ 180

=> $\frac{P_{2}\times 6\times 1}{100}$ = 180 - 75 = 105

=> $P_{2}$ = $\frac{105\times 100}{6}$ = $ 1750

Hence, $ 1750 must be invested at 6% so that the total return for both investments is $180.